When i turn the camera on, it cycles through

Sounds like there is some issue with the lens mechanism. Most probably something like a grain of sand fell into the cogs in the zoom mechanism (been taking pictures on a beach? ;). Dirt gets into the mechanism through the gaps between the zoom barrels and the camera body. One tiny grain of sand is enough to cause the lens mechanism to jam or malfunction.
Unfortunately, this is a problem with pretty much all compact zoom cameras. Usually there is not much you can do with this. First thing I try in cases like these is gently tapping the camera to shift whatever might be blocking the mechanism. If unsuccessul, then only way I know to fix this is completely stripping the lens to clean it or swapping the lens with one taken from another camera ("donors" available on ebay ;).
If you are not keen on tinkering with your camera I would suggest selling it on ebay - TZ3s with lens mechanism issues still fetch pretty good prices.
Sorry if this is not much of a help, but unfortunately there is no easy fix to this one.
Good luck,
Raf