It's hard to say what's wrong, so have my generic tips for narrowing down the problem:
- Try running Memtest86+ to ensure nothing is wrong with your RAM.
- Try running a live Linux distribution off of a USB stick to rule out any software issues, including driver issues.
- Check the SMART values of your harddrives, make sure none of them are failing.
On a related note, one of the (now replaced) machines running this website once had an issue with complete freezes. It was possible to wake it up by puhing any button on the keyboard, or by generating some other very specific IO interrupts. Other than that it would be completely frozen, even lagging the clock behind.