Gah, I had that issue once, annoying as hell getting CCC up and running.
Essentially, somewhere on the C drive, theres a hidden folder where windows keeps track of when DLL files are updated. As part of an install [say, for CCC], if the driver version has not changed, the DLL is not updated as part of the install.
What happened in my case was one of the DLLs somehow got corrupted, and clearing out this hidden folder caused every DLL to be reinstalled as part of the Catalyst install, which fixed the issue.
Problem is, I forget the name of the hidden folder where the files are stored; I'll see what I can find before I leave work today...
EDIT
Found it! See quote on second post on page.
http://forums.amd.com/game/messageview.cfm?catid=279&threadid=101834&enterthread=y&STARTPAGE=3
Goto "C:\Windows\assembly" and delete any keys with the token "90ba9c70f846762e" [the key ATI uses]. Now reinstall Catalyst. This forces every DLL to be re-installed, which should fix the problem with CCC not opening.