I have a Mac Pro model 1,1 which used to work with Ethernet pluged into either RJ45 socket. It now does not recognize either connection.
Since this could be physical or sortware, how can I further diagnose the problem?
Since you don't have the original disks (and therefore don't have Apple Hardware Test), I would try downloading AHT and running it from a USB. The steps to do this are as follows:
In the Terminal window, enter the following:
cp -r /Volumes/AppleHardwareTest/System /Volumes/AHT/
Now we need to make the USB flash drive bootable, so enter the following line in Terminal:
sudo bless --folder /Volumes/AHT/ --file /Volumes/AHT/System/Library/CoreServices/.diagnostics/diags.efi --label AHT
Enter your Admin password
Leave the USB flash drive plugged in and restart the Mac Pro
Immediately hold down the Option key
Select the AHT from the list and boot up
NOTE for other readers: - Both the Terminal commands and the download link used here were written for this specific question. Please do not follow these steps unless you're also wanting to download and use AHT for the Mac Pro 1,1 (i.e. these instructions will not work for other Mac Pro models).