A few simple (and free) things you could try:

Run a HDD diagnostic to identify & flag any bad sectors. I've experienced freezing a few times where the Swapfile resides over bad sectors.
Make sure the CPU heatsink gets warm i.e. it's making a good contact with the CPU.
Remove & reseat as much as you can (AGP, DIMMs, IDE cables etc.). Alcohol wipes are good for cleaning the AGP card & DIMM edge connectors.
In BIOS setup, load factory defaults. Additionally, you may also have a pre-defined Safe Setting which may help.

That leaves you about 999,990 other possibilities. Good luck and I hope you track it down