This could be any number of things. If the overnight Memtest86+ run comes back with no errors then I would next focus on either an overheating problem, faulty hard drive, or a dying power supply. What exact RAM do you have? Have you manually set the RAM speed/timings/voltage to their rated specs in the BIOS? That's very important, especially when running four sticks of RAM.
What are your idle/load CPU temps?
What HD do you have? Your manufacturer should have a drive utility that checks for faulty sectors.
What exact PSU do you have? I'm not aware of any quality units that have a 680W PSU. A POS PSU will cause all sorts of stability issues.