PC randomly reboots only when connected to network

I have run RAM tests, replaced the power supply, checked temps, reinstalled Win XP, gone through all the malware/virus removal stuff. My kids play old-school games on this machine, and when it's not connected to the network it runs fine, hours on end. They can play Diablo II all day without a hiccup.

Once it's connected to the internet, it randomly reboots. No BSOD, just a full restart even when I've set it not to. Running Win XP SP3, fully updated, P4 3.40GHz on an ECS 945P-A motherboard, 4GB RAM, GeForce 9400GT video card. I disabled the onboard NIC and plugged in a D-Link USB network adapter, same problem. It can happen in an hour or in 10 minutes, but eventually it does a full reset.

Any ideas?

 

By that, do you mean that you have Unchecked Automatically Restart under Startup and Recovery > System Failure?