To make sure it's not anything driver related, try a live CD (such as linux mint)
Once you successfully get it to work check the windows event log for anything suspicious.
Did you overclock anything? If so reset everything to their default timings for now.
Do you have another computer you could test the monitor on?
Also, if you do have another computer available you could try to enable the remote desktop connection feature (or install vnc server) to try and remote control the PC having the issue, the goal would be to check if the problem is related only to the display or if the computer completely stops working when it happens.
With the tests you've done so far we can probably rule out (PSU, GPU and RAM)
Likely suspects would then be (Monitor, Mobo, HD, CPU or software)
Edit : Try safe mode as well, if safe mode always work the hardware is probably Ok and something is wrong with windows (drivers issue would be likely)