If I hook the battery back up the way it was originally, it does turn on and, yes, also the battery charges.
But, because the battery is small, and old, the charge does not last very long --maybe 10 minutes at best.
If I plug the camera in with any 5v charger (even USB to my laptop) and the battery is not installed, it still turns on.
I tried several batteries, but cannot get it to turn on with any of them, unless it is also plugged in. Interestingly, the charging battery display on the screen shows that those batteries ARE charging though.
This is bizarre.
Thank You!