Upon trying to turn camera Panasonic DMC-ZS3 on, error message appears: system error (zoom). The lens comes out a bit and then goes back in, shutter closes, then lens comes out a bit again, then goes back...
I don't know that I can help you fix it, but I can try.
Here are my thoughts...
Check the battery first. If it's like a normal battery, like AA or AAA batteries, replace them and try turning it on.
If it's a flat lithium battery that you recharge using a power cord that plugs into the camera, you might want to buy a new one. Charge it fully over night and try powering the camera up in the morning.
You never mentioned what the error message was! So I can't help you there.
Next, you might try connecting the camera to your computer and see if it comes up. Also, check with Panasonic and see if there's a way to reset your camera. Maybe there's a way to do a software reset. Also check to see that there isn't a downloadable software upgrade or patch available. Lastly, you may want to consider Panasonic customer support/technical support, they may be able to better help you diagnose the issue with your camera.
I have a Lumix too. I have an DMC LZ10, my daughter has a DMC TZ3. They're similar in many ways, and yet they're different in many too. Mine uses AA batteries, hers uses a flat lithium rechargeable that uses a power cord. The internal software is pretty much the same (sort of). Enough so that I can work the settings on hers without having to reference the manual.
As a computer tech, my first impressions are that you're having either power issues, or software issues. Eliminate the variables.
Start with power and work your way out from there. If it behaves the same with any battery, you've eliminated the power issue. Now it's software. Simple enough?