For the desktop PC that's connected by ethernet cable but unable to get online, open a Command Prompt window ("Start > Run", type CMD and click OK) then, at the prompt, type...
...and press Enter. This will show details of all network adapters installed in the PC. Right click in the Command Prompt window, "Select All" and press Enter to copy the details to the clipboard. Paste the details into a forum reply here.
As you are unable to paste the details directly from the computer, because it cannot get online, paste them instead into a blank "Notepad" file, transfer the file to a working PC and copy/paste the details from there.