Chosen Solution
When I noticed that my camera battery was dead, I plugged the camera into the AC adapter to charge. However, the camera still will not turn on after charging the battery for several minutes.
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