HDCP compliance shouldn't be an issue when just trying to connect a computer to an HDTV.
@ thenumberwun - The issue you're having sounds to be a resolution, refresh rate issue. Your HDTV just cannot accept the output of your graphics card at it's current setting. I've had a similar issue with my HD4670 and my Olevia 232T 720p HDTV.
Here's a couple things you can try.
1) With only the HDTV connected via HDMI, try to boot your system into safe mode. If you're not getting an image at all during the boot process, this probably won't work. If you are able to get into safe mode, shut your system down, reconnect your monitor via DVI and reboot, once again, into safe mode.
Set up your displays in Extended mode and set the monitor as the primary display. Also, in Catalyst Control Center, under preferences (top right), set up a hot-key toggle to swap displays. Save it, shut down and restart your computer; this time, allowing it to boot normally.
You should now have your desktop on your monitor and the HDTV flashing purple/black as you previously described. Open Catalyst Control Center and run through the various resolutions on the HDTV until you find the best one to suit your purposes.
If that doesn't work then...
2) With only the monitor connected (via DVI), go into Catalyst Control Center (or whatever it's called now) and under preferences (top right), try to set up a hot-key to swap displays. Not sure this works with only one monitor connected.
Shut down your system and reconnect the HDTV via HDMI and restart. Since you can't see the desktop at this point, give your system time to boot up. If you need to log in, do so. Then use the hot-key toggle to swap displays.
This should give you the desktop on your monitor and allow you to adjust the resolution on your HDTV.
Hope this helps.