Actually, a couple of things you want to check:
Are you set to a resolution that the TV supports via HDMI? If you are using a newer Nvidia card, hook it up to a monitor and go into the Nvidia control panel and use the HDTV setup to select 720p as it should work for all LCD TVs.
Are you using just one display device? If you have a monitor and the TV hooked up, both need to be enabled.
Once you have set it up using a monitor, and ensured that your drivers are current and your connections are good, make sure that the TV is on, and selected to the correct HDMI input, and then turn on the PC. HDMI is the same standard as DVI, so it should work.