When I try to take a picture, the zoom lens won't move.

When I press the power button, nothing happens.

When I try to take a picture in flash mode, the flash will not go off.

There may be some debris stuck around your flash button itself. Try blowing on it or removing it gently with a cloth. If this does not work, try replacing the flash using this guide.

The simplest reason for this problem is an issue with the battery and charging system. Make sure you are using the proper USB charger and cord and they are not malfunctioning or damaged. If everything is working normally there may be an issue with your battery, which you can replace by opening the battery compartment.

There could possibly be debris stuck in the crevices of the zoom lens. Try blowing on this part of the camera or gently cleaning it with a cloth. If this does not solve your problem, there may be an issue with the motherboard. To replace the motherboard, you can follow this guide.