I have a very similar problem.
No matter what I try, I can't get my card to output anything on HDMI once I have the AMD drivers installed.
I wrote a long post about the problem, including everything I've tried, but I haven't been able to get feedback or assistance. You can read it here:
One thing your could try, that worked for me, to get video out of your HDMI port would be to installed Window's generic graphics adapter drivers.
1. Uninstall the Catalyst drivers.
2. From the device manager, go to your display adapter.
3. Right click on the 6850 and click "update driver software"
4. Select the "browse my computer..." option
5. Select the "let me pick..." option
6. Select the "Standard VGA Graphics Apapter" driver
7. Click next and finish the installation.
That will load the same drivers windows uses in safemode.
You will be limited to a lower resolution (no 1080p) and will have no hardware acceleration, but your HDMI output should work. At least, that's the only way I could confirm that my HDMI port isn't dead on my 5850.
Give that a try and please let me know if it works.
It's by no means a fix but at least you might be able to tell if your HDMI port still outputs anything.
If enough people are able to prove there's a problem with the AMD drivers and HDMI output they'll take notice and get around to fixing it... maybe.