The fact that the display does turn on, and off again, indicates to me (just a guess), that maybe a pin in your cable or output on your GPU is damaged slightly. Pretty much was it_dan_zsu said.
To actually certify that its your GPU causing the issue, take it out, and use your CPU to get display. If there are no issues there, you can single out the GPU as an issue. If the GPU is an issue, and worked fine on the CPU, then the cable can also be ruled out.