Your Mac is too old to support Internet Recovery. So it seems like you have three options:
A) You can dig the InstallESD.dmg out of the El Capitan installer app (see below), and burn that to a DVD Then, then boot off that DVD to wipe the hard drive and reinstall the OS.
or
B) Get another older Mac, that is running 10.7 thru 10.11. Boot yours with the T button held down, into Target Disk mode. Plug it in to anotherthe other Mac via Firewire. You can erase the drive from the other Mac, and then install El Capitan from there. Run the installer on the other Mac, and when you get to the screen where you choose the disk, just choose the disk of your Mac mini. Only Macs running 10.11 or older will let you run the 10.11 installer.
or
C) If you can'd do either of these, you could do a bit of a hybrid of the two. If you have access to another Mac that is newer, and you have a Thunderbolt to Firewire adapter, you can still boot the mini into Target Disk mode. Then from the newer Mac, erase the hard drive. Then partition the drive into one small 10 GB partition, and one bigger partition. Get the El Capitan installer, extract the InstallerESD.dmg image out of it, and 'Restore' it using Disk Utility, to the 10 GB partition. You can then reboot the mini off of that partition, and install the OS on the bigger partition. Once that is done and you're running off the new OS, you can go into Disk Utility and delete the smaller partition.
Option 3 is a bit more complicated but it should work. If you don't have access to ANY other Macs, or any install DVDs, then you might be out of luck until you can get access.
To get the InstallerESD.dmg disk image out of the El Capitan installer:
- Right click on the
Install OS X El Capitan.appand choose "Show Package Contents" - From there, navigate to
Contents/SharedSupport/InstallESD.dmg - Just drag that disk image to your desktop and work with it from there.