My ~10 year old XP box started to become cantankerous.
Unidentified hardware failure, intermittent, becoming increasingly frequent. Probably a loose connection somewhere in the maze between the CPU and the MB, but the tech doesn't know for sure.
Get a Linux LiveCD, many of those will allow you to run a memory test on the machine and possibly narrow down the issue. It's also worth just removing and replacing the RAM, in case there's a dodgy contact, and if that doesn't fix it, take the CPU off and replace it. Check that the fans are all working properly too, overheating CPUs or support chips get temperamental.