Could a screen go black after boot up or near boot-up due to the case Power Supply not putting out enough juice to run the computer when the OS comes on?
You can test your theory by unplugging a few devices and see if you successfully boot.
Remove power from optical drive (s), remove expansion cards (like video and sound if you have them).
Is the machine itself actually shutting down/restarting? Have you ruled out the monitor being faulty?