Firstly , try connecting your ac adapter or usb cable.
Try holding the shutter button while switching on the camera.
Look at the lens , and if some of the lens 'circles' is misaligned or not concentric then try wiggling it (while holding camera lens down).
Try gently pushing or pulling the lens when it extends but this is risky as it may cause the lens barrel to slip out of its guidance system.
Another way to do this is to place the camera lens down on a hard surface and then power it up. Be sure to use a soft cloth or something similar as to not scratch your lens or casing. Let the lens push the camera up and down a few times and sometimes the little resistance provided by the camera is enough to get things going again.
Try hitting your camera near the lens on the body with the soft tissue on the palm of your hand.
Other than that , I would take the camera to a repair center for a evaluation to see if it would cost more to repair than to replace the camera.
If it is still under warranty I would suggest you take it in before trying any of these steps and remove any off-brand batteries or accessories as some stores are really fussy about warranty repairs on camera's with non-brand accessories.