I have a lumix DMC-F27

Hi,

Do you mean DMC-FZ7?

I own one. Assuming that the camera is working normally, then I know two settings that will cause the zoom to be fixed.
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Suggestion No. 1:

If the zoom is fixed at the wide end:

1. Turn the mode dial to "P". Now turn on the camera.
2. Press "MENU SET".
3. Press the up arrow button.
4. Now, a menu item named "CONVERSION" should be highlighted. Press the right arrow button.
5. A sub-menu screen should now pop up, select and set "OFF".

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Suggestion No. 2:

If the zoom is fixed at the telephoto end:

1. Follow Suggestion No.1.
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Suggestion No. 3:

If none of the above solve the problem, then the lens might have been knocked slightly out of position.

~If the camera has been dropped.
~If the camera has been thumped or banged.
~If while zooming, the lens was obstructed.
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The zoom motor also could have died, it costs about $50.00 U.S. at Panasonic.com.
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My best advice would be to contact panasonic customer service.