What is the more likely cause of a PC freezing?

My father-in-law asked if I could take a look at his PC, he said it frequently locks up at different times. Sometimes, after a boot, sometimes after it has run for awhile. When it locks up, I've been able to hold the on/off (power) button in and it restarts.

Just trying to decide if I should try an XP re-install or start looking for new hardware.
Any tests I can perform?