Make sure you press the ON/OFF button firmly. Do not press it too quickly, otherwise the camera may not respond. If the camera power still does not turn on or off, press and hold the ON/OFF button for at least 7 seconds.
If the camera power is not turning on make sure the battery is charging correctly.
The camera may require service if the suggestions above do not resolve the issue. Begin the procedure to send your Sony product into a Sony facility to be repaired.