If a X20 camera fails to react to the "on switch" and the play button on the back it could be due to a faulty fuse on the main PCB.

If you suspect this is the case (likely if nothing else works, even with new / freshly charged batteries) and if you are confident to work on SMD boards follow the disassembly guide for the X20.

This will eventually give you access to the main PCB which is fitted to the battery compartment.

Remove the whole battery compartment from the camera, and unscrew the PCB from the chassis. It will then look a bit like this.