If you have a older Lumix that does not want to power on

As you know Panasonic issues Firmware Updates that can be downloaded online, and then installed using a computer and an SD card.
Some of those Firmware Updates made the cameras refuse to turn on if the battery was not an "approved" Panasonic battery.
This significant change was not publicly announced.
Panasonic Lumix batteries are available, but there are also dozens of different generic Lumix batteries available, and there is no reference source as to which generic batteries are "approved."
Therefore I would encourage you if you have a Lumix camera that is balking on startup to first try a genuine Panasonic Lumix battery that is fully charged.
You may find that the only problem was a generic battery that the camera did not care for.
(And of course many "Lumix" batteries sold online are not actually Lumix batteries, but merely counterfeits. They have Lumix markings and are often very good
imitations on visual inspection.)
Another reason some Lumix cameras will not power up is the memory card.
Sometimes people use a newer SDHC type card in an older Lumix, and the camera goes into electronic spasms trying to read the newer card. An older plain vanilla SD card will often solve the problem instantly.
If a Lumix camera is not powering up with a 8gb SDHC card there is a good chance it will power up immediately with a 1gb SD card.

I frequently recommend the Lumix TZ5 to people starting out, as it is a quality build, metal, not toy-like plastic, has more manual controls than most people will ever use, and the engineering is remarkable. I repair TZ cameras and donate them to homeless shelters and domestic abuse safe houses and college photography students and such, as they have full User Manuals available to download, full Service Manuals available for download in PDF format, have a very gentle learning curve, and produce photographs that are superior to many of the current cameras in the 600 to 800 dollar range. Yet a used TZ5 can be bought for 50 dollars or so.
Update the Firmware to v 1.2, never carry it in a leather camera case or pocket or purse or with any cloth of any kind, and you have a superb camera for many years.