Are you sure the shutoff is on the hot side? Usually it is on the cold (inlet side).
The energy has to be going somewhere. We know from Ohm's Law that if we are pulling current and have a voltage potential, that it is going to become heat (or some energy form). From your measurements, you are putting 2 kW into it, so something should be getting warm. It appears that:
1. The hot water is leaking somewhere (crossover to cold, etc.)
2. Element covered with deposits and slowing the heat transfer. Doesn't seem likely based on the age of the unit. It would still eventually get hot anyway. The assumes the the t-stat is working correctly and keeping the element going.
3. Relief valve - can you see where it goes? If it was sticking/dripping and directed into a drain where you couldn't see it, your HW could be leaving that way.