I have a similar problem. The opening clipboard comes up, but no response when I use the mouse to select online/offline/quit and so on. I am using 3.01 patch 0 on an SSD (which worked fine prior to Patch 1 coming out). Attempting to launch from Windows Start up menu made no difference.
Update: I also noticed that ctrl-alt-del stopped working in Windows, even after closing AHIII. I stopped and started the game several times from the shortcut, it recognized my mouse once then lost it again as I tried to duplicate the "fix". A reboot and several startups later the game recognized the mouse and I installed 3.01 patch 1. After the patch installed, I instructed it to start AHIII when prompted. Again the clipboard gave no response to the mouse or ctrl-alt-del within Windows. I rebooted again and confirmed I could activate ctrl-alt-del within Windows prior to starting AH. So far AHIII is working correctly now from the desktop shortcut. Hope this helps.