@shutterfinger: the M645 (the 1st model from 1975) and the 645ADFII (autofocus model from 2005) are totally different. The M645 does not have a detachable back.
But the link to the site with service manuals is interesting. I've bookmarked it. Thanks.
@Photo Chemist: I have the AFD iii and had a quick look at the back plate. It's attached with only 2 screw on the left side but maybe there are another 2 underneath the rubber of the grip. If you're going to attempt to open it up, get a proper screwdriver. The cheap small screwdrivers from the hardware store won't fit properly and you'll likely ruin the screws. The
Wiha PH000 screwdriver fits well.
If a DIY repair looks too complicated, you may want to give Capture Integration or KEH (both in Atlanta) a call. They might be able to give you a rough estimate on a repair job.
Good luck!