Eureka! We are getting close! I went to the site mentioned there, selected option 2 and downloaded Shexview.exe. I disabled all of the non-Microsoft Context Menu Handlers and re-booted. The problem remained: Every file (in Windows Explorer) or any icon (in the DeskTop) I right-clicked caused the computer to freeze and the sand glass appeared and stayed forever. I could still move it with the mouse but nothing else. I restarted and enabled all of the context menu handlers.
I then decided to go and disable all of the non-Microsoft elements listed (icon handlers, etc.) This time it worked! I went back and re-enabled them one by one until I found the culprit: It happened to be an Acronis True Image Shell Extension. I plan to contact Acronis and ask them about it.
Thank you so much for putting me on the right track! I don't believe I would have ever found the reason without your help.
I also want to take this opportunity and thank, again, all the people of this board who expanded effort on my behalf and tried to help me.
Oded