Hi
There may be any of the three fault in your device.
1) Battery got died up (Need to replace) 2) Your Charger may be faulty, try to charge it through USB Cable by connecting it to your system (computer), I case your camera have facility to charge it from computer. 3) ON/OFF switch may be malfunctioning (shorted).
Else, Your device need service (repair)
Have a nice day Rating the solution is highly appreciated.