There are many explanations for this problem, but lets start with the easiest. Make sure to hold the power button for a few seconds rather than just pressing it. Next, the problem can be the batteries. If you notice they are dirty or messed up in any way, replace them. Also, if you do not notice any problems with the batteries, try removing them and putting them back in the correct pole direction. Finally the last two solutions to the problem are making sure the camera is charged by attaching the camera to the charger, and the last problem is the most serious and may require you send the camera in for repair, a bad logic board. This is an important part of the camera and you may cause more damage than good trying to replace it if you are not experienced in doing so.