When turn on my PC, my monitor turns on then off at about the logon screen. The PC stays on. Turning the monitors brightness all the way down does not extend the duration. I have a HD 4850 graphics card that is hooked up via DVI. My power supply is a 650w and both the card and power supply are about 2 years old. I hooked up my monitor to my netbook via vga cable it has been on and working for about an hour with no signs of any problems.
Then you have ruled out that you have a faulty monitor if you have it plugged into your laptop. If the Pc stays on then it's a good chance it's not the power supply. That only leaves one thing , so how is your warrenty on the video card.