Steve and Deb,
MDL-10993 "Restore creates duplicate activity/resource icons with no text" sounds related. Do you see two icons for every activity/resource, one with text and one without, or just one icon without text? if you think your problem is related, please comment on MDL-10993.
Deb's solution sounds like a workaround. Normally it should be possible to just check what you want; backup should be able to figure out the dependencies. For example, if you check quiz, backup will take questions from the database.