How to diagnose Blue Screens in Windows 7 (64bit)

It sounds like a ram problem which means the BSOD won't be that helpful since it will be different programs depending on what is writing to the ram at the time. A good way to check would be to run memcheck86 which can be downloaded and written to a bootable CD or is included on the Ubuntu live cds. Try running it for a period of several hours to see if it comes up with any issues.