If your camera is currently frozen, try to reset the camera by holding the MODE button for 10 seconds (hold the top SHUTTER button on the HERO Session / HERO4 Session). Should the camera not prompt a reset, remove and then reinsert the battery to get it unstuck (for cameras with integrated batteries, Step 1 will imitate a battery pull). Make sure you have the most current software on your camera.
Remove the battery and the AC adapter (charger). Press and hold the power button for 3 - 4 seconds with these removed. Pop your battery back in, along with the AC adapter. If it still refuses to charge, you could be looking at a bad battery or possibly a bad charging circuit on the motherboard.