Yes, as long as it has the appropriate connections like you already said, it will work. First off, are you trying to connect the HDMI into the motherboard or GPU HDMI port? And have you tried a different HDMI cable? And make sure the tv is set to the correct input.
Well, if you already tried the cables, ports, etc...then it really seems to be a pc issue. So, I would say try the GPU in a different computer if possible. Or maybe in a different motherboard slot if you have other slots. If you still can't get it to work, then the gpu may need to be replaced...can't really say for sure.