A couple more things to try: Since you can't delete the new, duplicate icon, try dragging and dropping the old icon onto the new one. If it deletes, then, Voila!, you're down to a single bin.

Also, try going to Services>Personalization>Themes>Desktop Icon Settings (located in right side column) and uncheck the Recycle Bin Checkbox if it is indeed checked. Click apply - or cancel, if it isn't checked..

Jim.