After some digging and checking, I found out the real cause of one of the machine where the following symptoms exist:
There is no errors in installation on Catalyst 10.x. There is a Catalyst Control Center shortcut when you right click on desktop, but when you click it, nothing happens.
If you have the above, you may have the same problem as me.
Are you using a 64 bits OS? Have you previously installed a lower version Catalyst, such as 9.x or below?
Well, if your answer is yes to the above, it is VERY likely you have the same problem as me.
The problem lies in the bad uninstallation. In drivers before 10.x, there drivers were not properly written and installed as 64 bits software. Therefore, you will see some ATI folders and files in the "Program Files(x86)" directory. Inside there includes the faulty Catalyst Control Center. No matter how you reinstall your 10.x driver, it will go to the 64 bits directory "Program Files" instead and is never properly registered to run.
In case you still have no idea what I am talking about. You can do this to solve the problem:
1. Uninstall Catalyst completely.
2. Boot to saf mode if necessary
3. Remove the ATI directories in Program Files(x86) and in Program Files.
4. Remove ATI registry entries from both HKLM and HKCU.
5. Reboot and reinstall.
I can't believe it is such a screw up that had wasted so much of my time trying to troubleshoot this. I suggest a more through testing from ATI part for different scenarios for this installation which in the first place is already not a very clean solution and is often broken...