Actually the correct answer is to Uncheck " Use drop shadows for icon labels on the desktop. That's the one that did remove it.
I followed the advise from Saran008 and went to my Computer--right click--properties--go to advanced tab--click on performance and I tried first unchecking the boxes below as Saran008 suggested
1. Uncheck show shadows under menus.
2. Uncheck show shadows under mouse pointers.
but it didn't eliminated the shadows under icons or menus in the desktop but then if you scroll all the way to the end, you'll see " Use drop shadows for icon labels on the desktop." You need to Uncheck that one and it's done, gone!!