This is a known issue sometimes the two don't play nice and cause conflicts, Try using just the display driver and not installing CCC. Then you can use ATI Tray Tools for the stuff CCC would otherwise do.
Personally i have not run into the issue myself but know others who have and just having the display driver seems the way to go. Actually tell a lie i did have it running with just the Display driver once with my 3850.
You get much more control over the card with Ati Tray Tools anyway so your not loosing anything.