Re. Bad memory, I would have though that would just cause applications to crash rather than a re-boot ?
Yes, you quite often get blue screen stop errors with bad memory. You quite often get a reboot. Also, buried somewhere in XP's settings (I'm going to have to go and find it now!) is an option to 'reboot after stop error.'
Fast processor, fast graphics card, more than 1 HD - all these things consume more power and generate more heat. If your power supply is less than 400W you may get problems these days.
Just throwing a few ideas in the pot - if you have a few things to try in a methodical way it's a start!
Edit: The 'reboot on failure option' = System properties, Advanced tab, settings button