If you still have the install CD that came with your card then use those drivers for starters. After which, you can update as necessary at the AMD official site:
http://www.amd.com/us/Pages/AMDHomePage.aspx
If your not in the U.S, just replace the /us/ with your own country code.
From what your telling me, it looks like it's definetely your gfx card.
I've have the same problem with my HD5670 at one time.
check your hdmi cables to make sure thier not the culprit by using the hdmi output on your MB instead of your gfx card.
Also, try a after market hdmi equipped external dvd player such as; sony playstation 3/blu-ray player. Basically any hdmi equipped A/V device not attached to your computer. Also monitor your card in operation to diagnose any heat issues.
Do this by opening Catalyst Control Center, look to the lower left of this app, click on performance, in the drop down menu click AMD Overdrive, look to the left of the results page and you should see your GPU temp and fan speed.
Your GPU temp should never go above 60 degrees F. The higher the temp, the louder the fan attached to the cards gpu.
Take the side panel off your case and look at the fan on your gfx card in operation if possible. Make sure it's not obstructed by cahed up dirt. If it is, you may have to remove the fan, clean and grease/oil the ball bearings. If not possible, replace the fan.
This is how I've managed to keep my XFX HD 5670 in place for 2 years. As of this moment: 01/17/2013. I can run DMC 4 in DX9 at over 150 fps, averaging 135 fps/In DX10 I manage 100 + fps, averaging 89 fps. DMC 4 has a built-in program to test your gfx card. Accessible from the games home screen.
If all of the above fails, save up for a new card. Good Luck, BuB.