This happens when using any of the detection methods ATT provides? The one method has a "flicker" whenever it enables a profile and is the now-old method while the other does it instantaneously without flickers.
When I first installed my ATI card I had some problems (mostly things like waking up from standby causing issues, etc) but I went through and disabled all sorts of gimmicky things (like some "crash prevention" feature that CCC has an option for) and with the last drivers I used (8.4 as mentioned before) everything stabilized so I haven't bothered upgrading anything since and just go through creating game-specific profiles.
One idea to find out what causes the CCC not to start is to get procmon from sysinternals.com and monitor its process to see what errors it shoots out.