Probably Burned Heating Element
We bought a used sailboat last year. The PO had tied the cold water "in" tube to the hot water "out" tube the previous winter. Although we knew this had been done,we "forgot" during the anticipation of commissioning our new (to us) boat. Needless to say we quickly burned out the heating element when we turned the power on. And yes, the light on the breaker panel showed the tank was energized. West Marine ordered us a new heating element, all of $17.00. It was fairly easy to install. The new element was almost twice as long as the old element, but it did fit. The old element was coated with scale and other substances. I imagine the new, clean, larger element heats the water much faster than the old one did.
