Report the issue to iTunes, and also check out the troubleshooting article for video playback in iTunes.
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I just experienced this for the first time (after many successful rentals) last night. I rented a movie on my Apple TV 3 and pressed Play when I was prompted. For the first time ever, the movie did not start properly. It only displayed a still image while the audio played normally. I was able to scan through chapters, but still the image was frozen and only the audio played. After searching through forums, I was forced to take matters into my own hands.
I had noticed the movie was rented at 1080p resolution. I knew that my HDTV was only capable of 720p. So I put 2-and-2 together and thought that maybe it was a resolution issue; that somehow, iTunes did not recognize my resolution and downsample properly so that I was able to view it. Sure enough, I went to my Apple TV and went to:
Settings / iTunes Store / Video Resolution
Then I selected 720p. It was currently selected at 1080p. Sure enough, I reloaded the rental movie and all worked as usual!