If all that is wrong is the Ethernet port, you don't need a new motherboard. You can add a Ethernet card.
Maybe your problem is not the port on the motherboard, but somewhere else in the network.
Any ideas as to what I should try?
It would be helpful if you stated what exactly the symptoms are, what you have tried and any other information you have collected.
Have you checked the cable? Have you checked the link lights on both end? Have you checked the device that you are trying to communicate with?
If I had to go on just that the Ethernet port doesn't work, I would suggest getting any under $10 PCI Ethernet card from any local or mail order vendor. Of course, this assumes that the rest of the computer is working.
Possibly a bad cable. Given that you had the same problem more than once, I would check the other parts of teh system (e.g. the cable). I've had bad cables that work sometimes but then quit.