When you connect your TV through HDMI, check and adjust through ATI CCC the resolution so that it matches that of the TV screen before you play any video file.
What ATI CCC version are you on ?
If the above does not help, you may try uninstalling the ATI drivers, cleaning up ATI entries manually in registry, removing the ATI gfx card in Device Manager and reinstalling the drivers ATI CCC10.12. If still there is no resolution to your problem, then you may have to increase 2D clock speeds.
Let me tell what I have observed for my Sapphire Radeon HD5770.
Radeon HD5xxx series gfx cards have very low idle core/memory clock speeds, 157/300 MHz. When you want to play a video full screen, the gfx card tries to increase the core/memory clock speeds to something like 400/900 MHz to be able to play the video. During the process, the gfx card may stutter and fall down on what is technically called TDR ( Timeout Detection and Recovery ). In some instances, the gfx card recovers from TDR. In some instances, it cannot recover and gives you what you describe as a gray static looking screen.
If you have CCC 10.11 or 10.12, you can increase idle clocks from 157/300 to 400/900 MHz. This can be done with creating a profile and manually modifying the profile file. This may give you a peace of mind.