@paulaeiblum could be an issue with the zoom gear assembly or even a bad contact on the flex cables etc. Time to take a look at it. T works on your camera, go to this site [[Topic:Sony Cyber-shot DSC-RX100]] and scroll to Documents. There you will find the lvl 2 and 3 manual. #2 will show you how to work (assemble/disassemble etc) on your camera. For a lens repair, parts are usually hard to obtain. It may just be easier to replace the lens.
#3 manual has the schematic and that is useful if your lens is mechanically okay but your zoom still will not work. You would need to check things like IC202 on the SY-335 BOARD. That is the IC responsible for the lens control.
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