PC freezing and I've ran out of ideas !

I have an increasingly frustrating problem with my PC in that it regularly freezes. I've tried all of the suggestions that I've been able to find for similar problems in this forum – further ideas would be greatly appreciated!

Symptoms:
The PC freezes regularly, but with no obvious pattern of application, time lapsed etc. It can freeze during normal gameplay, browsing or office applications; it can freeze when the PC is idle (there are no screensavers or power-save options) and it has once froze during start-up before Windows XP has loaded.
There are other occasions where the PC can run for 4+ hours without a crash.

I’ve tried:
 Removing and re-seating the RAM.
 Swapping over the RAM cards
 Running Memtest86+ (no reported problems)
 Ran downloaded temperature monitoring software, with no indications of overheating
 Making sure that the hard-drive has more than 20% free space
 I have up-to-date Sophos anti-virus running
 I run Ad-aware and Spybot regularly
 I have all of the Windows XP patches and updates.

I’ve got as far as I can – can anybody suggest anything else to try ?