This is a really common problem, but having read all the other threads, I haven't found a solution. My old PSU stopped working (cheap, crappy brand), so I replaced it with a OCZ ZX Series 1250w PSU. Plugged everything in, but while everything spins up, there is no video. I tried both plugging the HDMI into the on board graphics and my HD 6950, no dice for both of them.
Is it possible that the old PSU took some components down with it when it stopped working?