PC rebooting randomly when connected to our wireless account

EMachine running Windows XP. Did a factory restore after son downloaded a virus. Since then, whenever this computer is connected to the internet via our Linksys Wireless-G modem, and ONLY ON OUR ACCOUNT (not on the neighbor's unsecured account!) it will randomly reboot.

No warning, no error message, it's just like someone hit the power button. Like I said, the timing is random. Does not appear to be linked to any kind of power saver, sleep, screen saver etc. mode. Could happen after two minutes, could happen after 20 minutes, it's random.

The computer has been taken apart, cleaned, checked for overheating (it's not), run for many hours with a shareware program called CPU Stability Test 6.0 with no found issues, and my son can play cd-rom games or be on the neighbor's wireless account all day without the problem occurring.

My husband and I also use another PC in the house with our wireless account with no problems, and the rebooting occurs on my son's computer whether the other computer is on or off, surfing the net or not - makes no difference.

We're stumped! Think you can figure it out?