Well, I don't think you need to run a full diagnostic test set as you say you are getting this problem in BIOS.
That rules out:
1. Hard drives (not being accessed)
2. Most of the RAM
3. Driver Conflicts
4. Sound/Video conflicts
5. Operating system problems
6. Applications conflicts
My favourite suspects at this point would be that your video card is on the way out or your power supply. Both can produce intermittent faults as well as just crash and burn ;)
Can you try another video card, it only needs to be good enough to work for testing purposes?
Are your MoBo diagnostics reporting correct voltages, and is the CMOS battery in good condition?