To check the the thermostate, turn of the power. Check the power supply at the water heater again then use a multimeter to see if you have continuity. It's probably not the thermostat in your case. The water is dripping from the pressure regulating valve. They rarely fail, a simple spring in the valve releases the pressure. I would recomend buying a water pressure testing gauge at a Hardware store. Just get a cheap one for $16. Instuctions and normal water pressure ranges will be included with the gauge. If you have excessive pressure you will need a pressure tank installed. If its normal than I would replace the valve.