I tried installing again, and it failed again. I'm getting an error message from CCC that says "No AMD graphics driver is installed, or the AMD driver is not functioning properly. Please install the AMD driver appropriate for your AMD hardware." I tried going back to the 13.12 drivers, but those failed as well when it got to installing the HDMI audio driver. It was a critical error that yielded a blue screen of death and prevented windows from starting at all. I had to run windows repair to get back in. I'll try the 13.4 drivers.
Paul, I really doubt it's a hardware issue. This is not a newly built system. I just re-installed windows in order to solve a different problem that was network related. The re-install fixed that problem, but seems to have caused a whole new nasty one. At any rate, the video card and drivers were working fine before the re-install.
Corroded, I've uninstalled everything. I used Display Driver Uninstaller to completely remove all ATI remnants from my system and tried a completely clean install and still no dice.