If your camera will not turn on, ensure that the battery is charged. It is a possibility that your camera may be unresponsive even while plugged into the AC adaptor. Your camera will not turn on until sufficient charge has been obtained. If the battery is charged, the camera could be overheated. If this is the case allow the camera to cool down in a place away from direct sunlight or sources of heat. For more helpful information about this problem or any other issues check out the Nikon Coolpix P530 Troubleshooting page here on iFixit.
Nikon Coolpix P530 Troubleshooting