My Nikon COOLPIX S51 Will not turn on.

Your problem may be due to weak/worn out batteries or corrosion on the battery contacts inside the camera which can prevent the full power of the batteries from flowing into the camera. Try this free fix before you do anything else: remove the batteries and wipe the camera contacts firmly with a dry cloth (heavy corrosion may require cleaning with a wire brush, steel wool, or sandpaper). Remove any residue that may have fallen into the battery compartment during cleaning, then wipe both ends of the batteries and place them back in the camera. This cleaning clears the problem about 90% of the time. If it doesn't work for you, your batteries may need to be replaced, or the camera may have a problem that requires professional repair.