Try removing the battery from the camera and then press and hold the power button for 1 minute. Release the power button, put a fully charged battery back in and see if it turns on normally.
If it still won't turn on, then either the lens servo motor is either no longer working or the lens has become jammed and the motor is not able to activate it. To fix this will involve having a camera shop open the camera and then if it is only jammed they can clean the tracks of the lens which will fix it. If the servo motor has failed, then it will need to be replaced.
If it is just a cleaning problem then it will cost about $50 to fix, if however it is the motor then you are looking at about $125 to repair it.
If the camera is less then 1 year old then the repair will be covered by warranty.