Is this a laptop or a desktop? With a laptop you will most likely need to hold the ctrl key and click whatever function button toggles the external display.
Have you made sure that your TV is on the correct HDMI source? Have another HDMI input to try? Or try outputting from the machine to the TV via VGA or DVI, if possible?
I've seen cheaper TVs require a complete power off (unplug power cable from the wall) to clear any odd issues.
Also, make sure that all of your display drivers are up-to-date, and if you would like to post your system model and specs that would be helpful.
Hope this helps.