A few monitors have a quirk that require you to start in VGA, then use the buttons to select HDMI input. Of course there will be no VGA display after doing that. Shut down and re-connect via HDMI. Try that first. Check the markings on the side of your HDMI cable to be sure it is at least ver 1.4.
If you are unsure of the GPU in your system, run GPU-Z in Windows to determine the exact model. Or run CPU-Z and click on the graphics tab.
GPU-Z: http://www.techpowerup.com/gpuz/
CPU-Z:
http://www.cpuid.com/softwares/cpu-z.html
Also when i run gpu-z it tells me that the name of my card is the amd radeon 7700 series. on my specs list it tells me my gpu is an AMD Radeon HD 7770 1gb