Does APPLE TV also provide you with the slightly older COMPONENT OUTPUTS??
HDMI can get locked out due to Copyright protection, but Component outputs will always provide a picture no matter what.
You've seen the 5 wire RCA jacks that take this cable on your Apple TV correct ? --
The solid colored ones create the picture, and the black ones are for sound. If you want to see if your TV is bad, or the Apple TV is bad, trying a DVD player on your TV would tell us if the TV is having HDMI problems or if the Apple isn't sending it's signal using HDMI.
And the Component cable delivers it's picture to the TV set completely differently. That helps us to start isolating where the problem is at.
So try some other boxes on your TV set and see if you get a picture or not.
Try the Apple with the component cables, or try it with a second TV and see what it does.
Just remember, the PROBLEM will always stay with the unit that HAS the problem.
If it's the TV....the problem will stay with the TV and it's HDMI connectors.