|I had this problem before with a client of mine, you know what it turned out to be. His HDMI cable was too fat and it wouldn't clear the PCI slot frame completely to plug firmly into the video cards HDMI socket.|
Please check this on your setup.
Other then that, we need to start testing your setup with other hardware, different cable, different monitor, Bluray player.
Do your have an HDMI on your computer monitor you could try?
Do you have any other HDMI output devices like a PS3 or DVD player or something, so that we know for sure that this is the computer an not something else.
Last bit, is if we check everything else and it is all good, then your video card needs to be replaced.