Have you tried with an external power supply? 8.4V power supplies are widely available and cheap. You will probably need an adapter to fit the socket on the camera.
Search on ebay (for example) for something like “8.4V 1A Mains AC-DC regulated Power supply”
and then for “8 in 1 AC DC Power charger adapter tips”.
But maybe check the switch first: the switch on the case can come disengaged from the “real” switch on the circuit board. That would explain the problem. But that involves opening the case. The service manual is available online, but doesn’t exactly match my FZ18. I would post a link to a blog where I describe how to open the case, but ifixit seems to dislike such links.