This is a very strange issue that happens to some users, but none has been able to find an exact solution that works for everyone so far. Well, there is one 100% solution, reinstalling the OS, but that's probably something people don't want to do.
Try the following method:
1. Reboot the computer.
2. Open Control Panel -> Programs and Features and locate the Catalyst Install manager. Double click it and select express uninstall all AMD software.
4. Download the official AMD Uninstall Utility. Run it and clean what remains.
5. Reboot to safe mode.
6. Use Driver sweeper/cleaner/fusion to clean whatever remains. You may use more of these programs after one another. (Note: This is a process that can harm your OS and is not recommended on a system that works fine. However, the alternative solution is reinstalling the OS, so you can do it without risking much.)
7. Reboot to normal mode.
8. Open My Computer and take a look at C:\Program Files and C:\Program Files (x86). If you find any folders with the name ATi or AMD, delete them, except if they belong to an unrealted program (Like AMD Overdrive, which is a separe install.)
9. Reboot again.
10. Download the .NET 4.5 installer and run it. If you already have .NET 4.5 installed, it will offer to repair it. Choose repair and let it run. If you don't have it, just let it install.
11. Reboot again.
12. Open Windows Update and manually check for updates. Install everything .NET related and generic windows updates you may not have. Don't forget the optional downloads section. Get .NET updates from there as well.
14. Repeat 12-13 until you have no more .NET related or generic windows updates available. Then reboot once more.
15. Download and install Catalyst 13.10 (or 13.9 if you really need that WHQL sig). Use custom install and make sure you have the display drivers and CCC listed as installable components. If not, stop here, and come back with a screenshot.
16. After the installation completed, reboot once more.
17. You're done. You have a good chance that CCC will work now.
18. If CCC still doesn't work, get your phone, call your geek frend, and ask them to come over and help you reinstalling the OS. Buy them a beer or whatever they like.
CPU: AMD Phenom II X4 810 @ 3120MHz | RAM: Kingmax 2x2GB DDR2 800 @ 833MHz| MoBo: MSI K9A2 CF v1.0 (BIOS: 1.D)| GPU: Asus HD 6850 1024MB (DirectCu) @ 835/1135MHz | Display: L24FHD | PSU: PC Power & Cooling Silencer 750 Quad | OS: MS Windows 3.11 Pro x64