Well, we finally got our IT department involved with this problem. They only sat up and took notice when we told them that we were going to have faculty request the Firefox browser be installed on their computers. FYI, to have a browser other than the district approved IE installed, all requests have to go thorough the IT director...
We knew the problem had to be in the settings, but couldn't find which ones. IT found them! Tools, Internet Options, Security, Trusted Sites, Sites. Add the URL for Moodle to the list of trusted sites (we have to remove the https check at the bottom of the list). Bob's your brother, the hovering will now work.