There are fundamentally two possible causes for your issue :
1) Onboard ethernet card is broken, so installing a PCI ethernet card should fix it, but you should be aware that your motherboard is starting to fail and act accordingly
2) Onboard networking controller is broken, in which case your motherboard is basically hosed
In both cases, the end result is that you are heading towards new motherboard time
... although you may be able to temporarily delay this by using a PCI ethernet card as suggested ...