Water Heaters - Water Heater hot but no hot water at tap

I have an under counter electric that's probably 10 yrs old. Hot water has been sometimes not hot. I changed top element and was hot for a couple of weeks. Went out totally and I changed out both thermostats. Was surprised when I removed thermostats that tank was hot to touch. After replacing still no hot water at tap. Now tank is hotter. Released relief valve and that pipe was hot. Water at ice cold at all faucets even water flow is very good. I'm stumped.

I have an under counter electric that's probably 10 yrs old. Hot water has been sometimes not hot. I changed top element and was hot for a couple of weeks. Went out totally and I changed out both thermostats. Was surprised when I removed thermostats that tank was hot to touch. After replacing still no hot water at tap. Now tank is hotter. Released relief valve and that pipe was hot. Water at ice cold at all faucets even water flow is very good. I'm stumped.

IF this is not a trick question I'll be most interested to see how you fix it. You said it is cold at ALL the faucets so I assume the water is getting bypassed in the tank somehow. Is there a bypass anywhere on the line?

It gets weirder. After I posted I turned off breaker thinking maybe I would try old thermostats again. I released relief valve again and thought I heard it running. Messed with it until it stopped, tried tap again water very hot.

This is a good one for the experts, I'll be waching to see their trouble shooting advice. larry