I'm working on the same issue with another computer of mine. I have cleaned out the computer and reseated the card. Card is still receiving power because the card's fan is still spinning. I hooked up a different computer to the monitor as well to make sure it wasn't a monitor issue.
Unfortunately I can't test the card in a different computer to see if it is the card. But If you are able to do that I would recommend that. If you are still having the same problem then it is most likely the card.
Right now I'm leaning towards it either being the graphics card or the Motherboard.
My card in question is an old BFG 8800. A lot of help the BFG lifetime warranty is to me now =). *sarcasm*