Well, you have killed 90% of the questions we would ask.... Good job, that's awesomesauce.
Wide plug to the motherboard is the main power source and the little one runs all the onboard devices (soundcard, onboard video, ethernet, ect).
Is there another 4-pin kind of plug that you can switch out and see if the plug is bad?
Does everything else on the motherboard work (sound and usb ports)?
There might be a setting in BIOS that could have been reset. Depending on your BIOS version, it might be laid out in a organised manner or it could be a older version that sucks to navigate. Within BIOS, Martian maybe able to help you out a bit more being closer to you.
If it was my computer, I'd replace the old PS and see if the Ethernet port works. Try to go back to your original hardware configuration so you can narrow down what the problem is. If it doesn't work with your old PS and no video card, then you might have lost the Ethernet adapter. If it does work with the old hardware, add the video card and see if the works. See if it's one or the other that is fucking with the Ethernet port. Could be an IRQ conflict or something else software related.
I'd try going back to orginal hardware specs and trouble shoot from there.
Also, if your port is dead, you are on your way to replacing a motherboard. Most of the time, when I see a port (ethernet, video, usb) on a motherboard go dead, the rest of the motherboard will slowly die. A PCI card will do you for a bit, but I'd be on the lookout for other parts going bad.