When I turn my DMC-TZ3 on, the lens open's up then shut'soff then open's again then shut's off again and a message appears saying shut camera off and try again, will not stay open why is that. The batterie is fully charge.

A recycling lens is usually caused by either a low or worn out battery (how old is your battery? If more than a couple years, it would be definitely time for a new one. Here's a selection.). If a new battery doesn't help (but it really does sound like you need a new battery), the next problem that could cause this is a lens error. Unfortunately, many cameras that fall prey to lens error problems can only be corrected by professional repair. But, here are some last resort troubleshooting steps that you can try that may correct it. They only seem to work for less than 40% of the lens errors, but if the camera is out of warranty (or repair cost approaches that of the camera), they're worth that try.