Percussive maintenance...
Really, if you've tried everything and are about to throw it out then try one last thing and risk it all....
Hold the power button to turn it on then, while trying to zoom the lens, give a firm whack with the palm of your hand on the back of the camera.
Sometimes the bit of grit or the gear that is not quite meshing is bumped out/in and then all is good.
Sometimes nothing happens, but you were going to trash it anyway and still can...
Sometimes you break something else..
I have
fixed 2 p&s and a bridge camera this way,
broken none.
Maybe I am buoyed and biased by my success to date...Ymmv.