This is an old thread, but it's one of the top search results for "ccc won't run" so I wanted to post another possible solution here. My solution was to clear out the Windows GAC (Global Assembly Cache). In Windows 7, you can browse directly to "C:\Windows\assembly". Sort by "Public Key Token", then delete everything with the Token "90ba9c70f846762e" (ATI's key). You'll obviously need Administrator privileges. No reboot needed either. Reinstalled CCC and it ran perfectly!
The GAC lets you share DLL's that are the same version number. If it's in the GAC, any installer will NOT install a new DLL - it'll use the one in the GAC. If the GAC DLL is corrupted, you're majorly SOL.
When I reinstalled the CCC, it took longer to install then it had before. Presumably, this was due to the installer copying all the correct DLL's to my hard drive. And no ATI DLL's have made it back into my GAC.
To give credit to the original poster, here's the page I found this fix on:http://www.hardwareheaven.com/mobility-radeon-drivers-support/186707-problems-installing-catalyst-control-center.html