I now have a working D200, and it never went in for service. Here's what I did:
I followed one poster's advice and drained the battery completely in another camera (I followed the advice of connecting it to a PC and then copying files back and forth to the card; time lapse with a flash also worked).
I charged the battery completely. (At this point, when I put it in the camera, the problem wasn't resolved...)
Let the camera sit for about 36 hours. This, per the local camera shop guy, thought this would "drain the capacitors". Whatever.
NOW when I put the battery in, all is well. (For now...)
Thanks for all who offerred help, and I hope this little journey helps someone else.