Yes it does. Both the shortcut and the icon under the file location. I tried starting Run as Administrator and as soon as I click Download Latest it responds (Not Responding).
I have also tried the Portable Edition and get the same problem. The only way the program works is by reinstalling it and allow it to launch as part of the install.
Have you tried added exclusions for CCEnhancer in any anti-virus/fireware software you have installed? It sounds as though something is interfering with it.