Have you tried using a cable release to rule out a problem with the shutter button? That would at least take one thing off the list of possibilities.
I had a problem with the multiple exposure lever a few years ago that gave me fits during an event, but it was one of those "suddenly started working again" things and never happened again. What I think I remember doing is something you've probably already tried. Wind on with the multiple lever forward, but don't shoot. Flip the lever back and then shoot. Then wind on normally and see if it works.