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.
Your can download the service manual here: http://elektrotanya.com/panasonic_dmc-fz18.pdf/download.html Have you tried with an external power supply? 8V4, 1A power supplies are widely available and cheap, although you only need 500mA, I think. You may need a barrel adapter, but sets of those too are available and very inexpensive.
I have probed my A701A and looked at one of the relevant patents. My provisional schematic is here . As I say there, it is only guesswork based on probing with a simple multimeter without C and H ranges in circuit. On my machine, it has become clear that the only problem was that the "points" (the centrifugal switch) no longer closed when the motor was not running. It was easy to remove the retaining screws and bend the copper support a little. The relevant patent (best in pdf) is US3701935.pdf. I can't for the moment find where it was freely available, but avoid some of the suspicious sites that seem to want to charge or collect information to download it. That patent by Prof Collie is about adding a triac to the circuit precisely to reduce wear on the "points".
