It is possible that the flash unit has failed, but not many do.
Your camera may (or may not) still be under the Panasonic 1 year warranty. You should find out the date of purchase.
I suggest you first, recharge the battery.
The flash draws more power than the camera itself, so you may just have a weak battery.
You also should check to see what scene mode you are using.
Some modes disable the flash.
See page 38 and the chart on page 39 of the camera Operating Instructions.
In the Set-Up menu (page 20) there is a Reset command (page 22).
The reset command should reset any unusual setting that could have been accidentally set.
Hey, I have a Panasonic Lumix DMC-FX35 and all of the sudden it just stopped flashing when I was taking pictures... I didn't drop it or anything like that, it just stopped using flash. I've tried resetting the format, turning the settings to flash and everything else that I could think of doing... Anyone have any advice? Thanks