Water heater is not working after a power outage

need a meter to test circuit for damage

Did you test elements for continuity?

reset circuit breaker fully off the on
power outage can call surge
check fuse on circuit board

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If unit has electronic control valve, then simple power outage surge can but out electronics.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#blower

Gene
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replace it with the same thing but newer

Water inside tank-type water heater can remain hot for some time.
That's one advantage of well-insulated tank-type water heaters.
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

Power outage can be related to failure of gas control.
Unplug stuff when power goes out. And then plug back in after power is restored.
Water heaters with electronics are not protected from surge.
Electronics can blow out during and after power outage. For example nearby lightning strike will cause current to run along household wires. With ordinary power outage, once power is restored, the surge can affect all kinds of electronic circuitry such as timers, water heaters, water softener, treadmill etc.

Sounds like you have intellivent gas control valve:
Open following link to identify gas control, and download typical manual, and download intellivent service manual with troubleshooting, error codes, etc.
http://waterheatertimer.org/How-to-adjust-temperature-on-water-heater.html#intelli

Take a moment and vote on answer:
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You posted under tank-type electric water heater.
1) Check the circuit breaker.
2) Open top cover located on side of tank and push in reset button.
3) If these two actions do not restore function, then open following link for complete troubleshoot:
http://waterheatertimer.org/How-to-troubleshoot-electric-water-heater.html

you need to unplug the unit, wait for 30 seconds reset the temp to the lowest temp, then try it, if this does not work it might have done something to the circuit board, are you on a gfi out let it needs to be there is water and ele, and should be on the gfi with a reset on it,,

What type of heater is this? I need to know the model name and make and then we can go threw the process of how to do it. Most gas heaters do not have power to them and I only know of a few tankless heaters that do.