This answer modifies the install procedure used by the OP in the following ways.
The Debian installation ISO files can be burned to a DVD. These DVDs are configured to be either BIOS or EFI booted. However, early Intel Macs, such as the OP's, can not boot from a DVD with such a configuration. Also, not all Intel Macs can BIOS boot from an USB port. This would include the OP's model Mac.
A brief outline of the procedure is given below. A rather lengthly explanation will follow.
The steps to install Debian are as follows.
Use another computer to download the current 32 bit Debian installation ISO file which includes additional software for graphical video hardware. This file can be found here. At present, this would be the file named firmware-10.7.0-i386-DVD-1.iso
. Here, the assumption have been made that all files are downloaded to the users default Downloads
folder.
Transfer the 32 bit Debian installation ISO file to a USB flash drive. Insert the flash drive a USB port. Use the following instructions based on the type of operating system.
OS X (macOS): Use the diskutil list
command to determined the device identifier. If the disk identifier is not disk1
, then make the appropriate substitution when entering the first line.
DISK=disk1
diskutil unmountdisk $DISK
sudo dd if=~/Downloads/firmware-10.7.0-i386-DVD-1.iso of=/dev/r$DISK bs=1m
Linux: Use the lsblk
command to determined the device identifier. If the disk identifier is not sdb
, then make the appropriate substitution when entering the first line.
DISK=sdb
sudo umount /dev/$DISK*
sudo dd if=~/Downloads/firmware-10.7.0-i386-DVD-1.iso of=/dev/$DISK bs=1M
Windows: A third party tool will be required. One such tool is rufus. For example, if a volume on the flash drive has been assigned the drive letter E:
, then the current version of rufus should be configured as shown below.
Note: A flash drive can be selected even if the drive has not been assigned a drive letter.

When finished configuring, select the Start
button. When the popup shown below appears, select Write in DD Image mode
followed by the OK
button.

Note: After successfully transferring the firmware-10.7.0-i386-DVD-1.iso
file to a USB flash drive, a partition on the flash drive may be mounted and modified by Windows. While these modifications will not interfere with the installation of Debian, the modifications will prevent verification of the flash drive by a SHA checksum or comparison to the original file.
Other possible third party tools are outlined in the "In Windows" section of the Arch Linux document "USB flash installation medium".
Create a MBR Partition Table on the internal drive. Insert the flash drive in a USB port of the Mac where Debian is to be installed. Start or restart the Mac and immediately hold down the option key until the Mac Startup Manager icons appear. Choose the external drive icon with the label EFI Boot
. When the image below appears, pick Advanced options ...
, then select ... Rescue mode
.

Continue until a similar image to the one below appears. Pick Do not use a root file system
, then select Execute a Shell in the installer environment
and finally, <Continue>
.

Enter the following commands. When asked to continue, enter a y
.
parted /dev/sda mklabel msdos
parted /dev/sda mkpart primary hfs 1mib 100%
reboot
If the Mac does not boot from the flash drive, then restart the Mac and immediately hold option key until the Startup Manager icons appear. Select the external drive icon labeled EFI boot
.
Install a 32 bit BIOS booting Debian. When the image below appears, select either Graphical install
or Install
. Here, Install
was chosen, as shown below.

Continue with the installation. When an image similar to below appears, select <No>
.

When an image similar to the one shown below appears, select Manual
.

When an image similar to the one shown below appears, select the line containing (sda)
.

When an image similar to the one shown below appears, select <Yes>
.

When an image similar to the one shown below appears, select the line containing FREE SPACE
.

Here you want to create a new primary partition at the beginning of the available space. When asked for a size, enter a size smaller than the maximum size. This value can be determined by subtracting from the maximum size the desired size of the swap partition and the size of the temporary partition needed for the 64 bit Debian installation files. In this example, the swap partition will be 6 GB and the temporary partition will be 16 GB. The difference is shown below.
128.8 GB - 6 GB - 16 GB = 106.8 GB
The size value you will enter most likely will be different from the value of 106.8 GB
entered in this example. Configure the rest of the partition settings as shown below, then select Done setting up the partition
.

When an image similar to the one shown below appears, select the line containing FREE SPACE
.

Here you want to create a new logical partition at the end of the available space. When asked for a size, enter the desired size of the swap partition. For this example, the value was already stated to be 6 GB. You should enter the value you have already determined. Configure the rest of the partition setting as shown below, then select Done setting up the partition
.

When an image similar to the one shown below appears, select the line containing FREE SPACE
.

Here you want to create a new primary partition from the available space. When asked for a size, do not change the value shown. Configure the rest of the partition setting as shown below, then select Done setting up the partition
.

For this example, the result is shown below. Select Finish partitioning and write changes to disk
.

When an image similar to the one shown below appears, select <Yes>
.

Proceed with the installation. When an image similar to the one shown below appears, either choose a mirror or avoid using a mirror. In this example, the mirror is avoided, thus decreased the time required to install. Avoiding the mirror can be accomplished by selecting <Go Back>
, then selecting <Yes>
.

When an image similar to the one shown below appears, probably the only software required is the standard system utilities
. In this example, a Debian desktop environment
will be omitted to decrease the time required to install. The SSH server
will be included, so sftp
will be available to transfer files later. Below is the configuration used in this example. When done making choices, select Continue
.

Proceed with the installation. If an image similar to the one shown below appears, select <Yes>
.

When an image similar to the one shown below appears, select the line containing /dev/sda
.
Note: When using earlier version of the Debian installer, the device /dev/sda
needed to be manually entered.

Finish installing Debian.
Create a 64 bit Debian installer on an internal drive partition.
Note: The instructions given in this step were derived from section 4.3. Preparing Files for USB Memory Stick Booting of the Debian GNU/Linux Installation Guide. The main difference is a partition on the internal drive will be used instead of a USB memory stick (flash drive).
Start by booting to Debian. If the Mac does not boot to Debian (via Grub) by default, then restart the Mac and immediately hold option key until the Startup Manager icons appear. Select the internal drive icon labeled Windows
. If a Debian desktop environment was not installed, login as root. Otherwise, login using the default username, open a Terminal window and enter the command shown below.
su --login
Enter a following command to permit writing to the /dev/sda3
partition, which has been assigned the /installation
mount point.
chmod a+w /installation
Transfer, to the /installation
mount point, the three files required to install a 64 bit Debian. One of these files is the current 64 bit Debian installation ISO file which includes additional software for graphical video hardware. This file can be found here. At present, this would be the file named firmware-10.7.0-amd64-DVD-1.iso
. The other two files are the text based installer image files required when booting from the internal drive. At present this would be vmlinuz and initrd.gz. Below are various ways to transfer these files. Choose one way or find another way.
Note: A choice below can depend on which predefined collections of software are currently installed.
- Use another computer to download and transfer the files to a FAT formatted USB flash drive. Use either the
cp
command or the Files application to copy from the USB flash drive to the /installation
mount point.
- Use another computer to download the files. Use
sftp
on this other computer to transfer the files to the /installation
mount point on the Mac. Enter the command hostname -I
on the Mac to get an IP address.
- Use the FireFox ESR application to download the files from the web. Use either the
cp
command or the Files application to copy the downloaded files to the /installation
mount point.
When finished, shutdown the Mac. If a Debian desktop environment was not installed, then enter the command below instead.
shutdown -P now
Remove any USB flash drives that may be plugged into the Mac.
Replace the 32 bit Debian with a 64 bit Debian. Start by booting to Grub. If the Mac does not boot to Grub by default, then restart the Mac and immediately hold option key until the Startup Manager icons appear. Select the internal drive icon labeled Windows
. When an image similar to the one shown below appears, press the C key.

Enter the commands given below to boot from the /dev/sda3
partition. This sequence of commands was derived from section 5.1.5. Booting from Linux using LILO or GRUB of the Debian GNU/Linux Installation Guide.
insmod part_msdos
insmod ext2
set root='(hd0,msdos3)'
linux /vmlinuz
initrd /initrd.gz
boot
Proceed with the installation of Debian. When an image similar to the one shown below appears, select Manual
.

When an image similar to the one shown below appears, select the line containing #1 primary
.

Configure the partition setting as shown below, then select Done setting up the partition
.

For this example, the result is shown below. Select Finish partitioning and write changes to disk
.

When an image similar to the one shown below appears, select <Yes>
.
Note: This is the point where the 32 bit Debian is deleted.

Continue with the installation of Debian. When an image similar to the one shown below appears, select the line containing /dev/sda
.
Note: When using earlier version of the Debian installer, the device /dev/sda
needed to be manually entered.

Finish installing Debian.
Remove the partition with the installation files and extend the Debian partition.
Open a Terminal application window. Enter the commands given below.
su
sudo parted /dev/sda unit s \ print
The output produced in this example from entering these commands is shown below.
dma@debian:~$ su
Password:
root@debian:/home/dma# sudo parted /dev/sda unit s \ print
Model: ATA VBOX HARDDISK (scsi)
Disk /dev/sda: 251658240s
Sector size (logical/physical): 512B/512B
Partition Table: msdos
Disk Flags:
Number Start End Size Type File system Flags
1 2048s 208592895s 208590848s primary ext4 boot
3 208592896s 239937535s 31344640s primary ext4
2 239939582s 251656191s 11716610s extended
5 239939584s 251656191s 11716608s logical linux-swap(v1)
From the second row of entries in the above table, record the entry in the End
column. This would be the row where the Number
entry is 3
. In this example the entry in the End
column is 239937535s
. The entry you will record will most likely be different. Next, enter the commands and entries shown below. Replace the entry of 239937535s
with the your recorded entry from the table.
sudo parted /dev/sda rm 3
sudo parted /dev/sda resizepart 1
yes
239937535s
sudo parted /dev/sda unit s \ print
The output produced in this example from these commands and entries is shown below.
root@debian:/home/dma# sudo parted /dev/sda rm 3
Information: You may need to update /etc/fstab.
root@debian:/home/dma# sudo parted /dev/sda resizepart 1
Warning: Partition /dev/sda1 is being used. Are you sure you want to continue?
Yes/No? yes
End? [107GB]? 239937535s
Information: You may need to update /etc/fstab.
root@debian:/home/dma# sudo parted /dev/sda unit s \ print
Model: ATA VBOX HARDDISK (scsi)
Disk /dev/sda: 251658240s
Sector size (logical/physical): 512B/512B
Partition Table: msdos
Disk Flags:
Number Start End Size Type File system Flags
1 2048s 239937535s 239935488s primary ext4 boot
2 239939582s 251656191s 11716610s extended
5 239939584s 251656191s 11716608s logical linux-swap(v1)
The first partition in the new table should now occupy the space previously occupied by the third partition. Next, enter the command given below to expand mounted filesystem to fill the partition.
sudo resize2fs /dev/sda1
The output produced in this example from entering this command is shown below.
root@debian:/home/dma# sudo resize2fs /dev/sda1
resize2fs 1.44.5 (15-Dec-2018)
Filesystem at /dev/sda1 is mounted on /; on-line resizing required
old_desc_blocks = 13, new_desc_blocks = 15
The filesystem on /dev/sda1 is now 29991936 (4k) blocks long.
The computation below can be used to verify the space used by the filesystem in blocks matches the number of sectors in the partition.
29991936 blocks * 4196 bytes/block / 512 bytes/sector = 239935488 sectors
Finally, enter the commands given below to close the Terminal window.
exit
exit
Restarting the Mac would be recommended.
If a BIOS booting Debian is the only operating system installed on a Mac, then the Mac should automatically boot to Debian. However, if BIOS booting has not be set as the default, there may be a delay before booting begins. Otherwise, the Mac Startup Manager can be used to boot Debian. To set BIOS booting as the default, boot from an OS X (macOS) installation DVD or USB flash drive, open a Terminal window and enter the command given below.
The version of OS X (macOS) chosen must be compatible with your Mac. The instructions for creating a Snow Leopard (OS X 10.6) installation USB flash drive can be found here.