Can motherboard cause network connection problems??

Hello all,

We have 7 Dell Optiplex GX260's in our small office and the strangest thing is happening! 

These computers were purchased Dec.2002 so are quite old.  We started having intermittent network problems on some PCs a few weeks ago.  We have a Dell PowerConnect 2324 switch and recently purchased a new PC 2724 switch.  We were able to move 3 PCs to the new switch just fine however 4 computers will not connect on the new switch.  Have confirmed that all ports work on the new switch and again cabling is fine. 

On one of the PCs in question we installed a 2nd NIC but same problem still occurs.  When the computer is off we see the link light however as soon as the computer is turned on they loose the connection to the new switch.  I upgraded the bios for this computer but still no go.

I spoke to Dell tech support for the switch side of things and they felt that it might be a motherboard issue causing this problem and to talk to desktop support.  Our warranty is done for the workstations so am posting a question here.

Has anyone come across this issue?  Any suggestions on what to try?

Thanks so much in advance for any assistance provided.