1) Make sure the tank is full and the bypass is set so water goes thru the hot water heater. (failure to fill can burn out the electric element in under a minute) To check from the outside feel for heat and if cool, pull the lever on the pressure relief valve with the pump on. Should spit some water out at you.
2) Listen at the outside as someone turns on the heater (electric and gas). You should at least hear a click as it switches on. If not, use a multimeter to check for voltage.
3) If you put it on gas, you should hear multiple clicks as it tries to light. If it's the first time since propane ran out, it may take a few tries before propane clears the air out of the line (after a minute or two without lighting, it will give up to protect the unit). Once lit, you should feel hot air from the chimney.
4) If you put it on electric, you should still hear some noise as the heating element kicks on.
Some simple potential issues:
- Check the breaker is not tripped and the 12 fuse is not blown.
- Make sure the switch is on (possibly an external one also).
- Depending on brand, there might be a reset in the outside panel.
- Make sure propane is turned on and you have propane (try lighting the stove burners to check)
90% chance one of these items fixes the issue.