Your statement "I've put fresh batteries in multiple times" brings up a potential problem.
That camera came with a Panasonic Lithium Rechargeable battery.
Panasonic is implementing a new feature that prevents using any other brand of battery in their cameras.
Are these "batteries" you are using made by Panasonic?
You should contact Panasonic about any battery problems.
I've got an Exilim FH-20, and there's something wrong with it.
I've put fresh batteries in multiple times, and after only a couple of shots it starts saying that the batteries are empty and then shuts down. It works perfectly when I plug it into the power mains though. I suppose something is wrong with the battery compartment connections or something, but I can't see anything amiss.
I updated the camera firmware, just in case, but no change.