If you're not getting any errors or warnings in the logs, then my next step would be to run the sysinternals process monitor and check what activity occurs when you click on one of the dead desktop icons. Is the mouse event not getting through, mouse coordinates not matching the icon positions, some other weirdness? Sorry, I really can't think of another way to troubleshoot other than with procmon, unless you have access to Windows debugging tools and can watch the Windows message queue and see whether Explorer is picking up/dispatching the mouse events properly.
One other thing... When the desktop icons aren't working, have you tried tabbing your way to the icons and then using the arrow keys to navigate to an icon and the enter key to launch it (assuming you can get the icon to grab the focus)?
Geoff
