Thanks for your suggestions, but nothing worked.

I'm reasonably certain that the problem had nothing to do with emptying my
Temporary Internet Files folder, since I didn't.

I simply created a shortcut on my desktop for a newly visited web site and
IMMEDIATELY dragged it into one of my desktop folders. That's when the
distinctive favicon for the web site shortcut changed into the "Big Blue E"
IE icon. When I dragged the shortcut out of the desktop folder and back
onto the desktop, the distinctive favicon was restored.

I did download FavOrg, and ran it as suggested, but it didn't help -- which
didn't really surprise me since I've never had a problem with the icons
appearing in my Address Bar or Favorites List, even after cleaning out my
Temporary Internet Files folder.

It's when I try to drag them off the Desktop that the problem arises.

Does anyone else experience this problem ???