Sounds too me like two issues either defective memory or a hd that may be starting to go. There is utilities on the web that can test both. Usually defective areas in a memory module cause the PC to lock up. I have seen a bad HD cause a pc to reboot, but usually the "Blue screen of Death" comes up first.
Could also be the motherboard I believe Asus had a history in the past of bad capacitors on the motherboard. Look for caps that appear to be bulging at the top. this is often a dead giveaway.
Oh.. and for every computer nerd out there.
http://www.dealextreme.com/details.dx/sku.21997