When I left-click on the Computer icon on the desktop or in the Start menu (or right-click on the icon and then select Open), I'm immediately returned to the desktop. Speaking with MSDN tech support they tell me that my operating system is definitely hosed. And that I should do an "in-place upgrade" to re-establish a full operating system. So I tried.
It took about 10 hours but at the end asked me to reboot. I did so. And discovered that the operating system was gone. Fortunately I had made multiple backups on a secondary hard disk close onto external USB disks. I was quite fortunate. Not only was the operating system hosed but the entire partition table was gone as well.
I use Acronis for my backups and it asked where to restore my backups. There was no C: drive. I ended up having to reinstall the operating system Windows 7 Ultimate on a machine that was initially running XP Professional and had been upgraded to Vista Ultimate and then to Windows 7 Ultimate. So I did a fresh install onto the un-allocated space that had been my C: drive. It took a long time but it successfully restored my missing drive.
So the question still exists: what is causing my Computer icon to not function?