Since it only reboots when you are playing LAN / ESF ingame. My bet that the problem is related with your video card. When it's over heated, the computer reboots automatic out of security reasons. How do i know? I have the exact same thing, my GeForce 2 GTS Fan is broken. And when playing games for a while, computer reboots automatic.
As said, it's your video card. Check if the FAN is working, if not. Get a new fan or a new video card.