Your tank should be filled to the brim, and only water should come out the relief valve. Put the water pump on until it stops, all taps closed. Open the relief valve. You should get water only.
You have had the unit for quite a few years, so you know about bypass valves and winterizing valves. Some units have a check valve on the outlet of the tank. It's only about 3/4 of an inch long. It could be frozen shut and your tank is not filling, but when you are off bypass and on tank, if you get water out of the hot tap it has to come through the tank.
Another option is an insect nest in the burner tube. Sometimes this ignites inside and will heat the fusible link and open it. Look for a wire with what looks like a fuse in front of the outlet of the burner tube. My fusible link had a corroded connection at one end and caused the heater to not start at all.
