Lzoom lens goes out and in, immediately, then camera turns off
Pull the battery and plug the charger into the camera. It should turn on and take pics now. If it does, you need a new battery!
Yeah, I know, the battery shows fully charged but it's weak and old so it really doesn't have the current to drive the lens.
Try to clean the battery terminals with an abrasve pencil eraser, (old red eraser #2 pencil from grade school) and wiggle the battery in the camera (gently) to clean the terminals inside the camera.
Let the camera charge the battery completly, (not in the dock!) and see if it turns on.
If it does, you will probably find that it discharges VERY quickly.
Buy a new battery! That extra battery that you have had since you bought the camera is probably also shot! They do have a shelf life!
If the camera does not turn on with just the charger, (no battery) then it's probably a lens error, but you should see an error code if it is.