I have a very similar problem. Out of curiosity, are you using HDMI to connect your monitor?
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 find a solution. You can read it here:
It looks like you've figured out the same thing I have, the only drivers that don't kill your video output is the generic windows drivers.
In the meantime, you can force windows to use those drivers until AMD fixes theirs.
1. Uninstall the Catalyst drivers.
2. From the device manager, go to your display adapter.
3. Right click on the 6670 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.
You will be limited to a lower resolution (no 1080p) and will have no hardware acceleration, but at least it proves your card works.
Can you please submit a bug report to AMD to help make them aware of this issue?