Was the system stable before you installed Catalyst? If you don't enter CCC, will the system boot properly and then operate normally?
I would suggest removing Catalyst completely, make sure all of your other drivers and Win7 are up to date, and then operate with the Win7 default drivers to verify overall stability. Then I would re-install Catalyst 10.5 operating at the default speeds (no overclocking).
This will verify whether you have a system stability or a Catalyst problem. Only after verifying all is well, should you start tweaking your CCC/Catalyst settings.