We have no hot water, and the DSI light is on. Doesn't work in either electric or gas mode.

Probably not. The gas control would have to have a knob that says on-off-pilot, for the hand lighting option to work. If it only says on-off, then you need the electric ignition to light it.

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http://waterheatertimer.org/How-to-test-water-heater-element.html
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It sounds like your thermal coupler needs to be replaced or maybe just cleaned. P.S. have you tried a different LP tank If its new or the person didn't pressurize the tank when filled you may not have pressure enough to keep the water heater lit.

Check for a bad fuse in panel first, then with a 12 volt test light or multimeter, check for power in to switch, as well as out when in on position if it's easy to get to. If not, turn switch on and test for voltage at brown wire to thermostat terminal, that comes from inside at back of water heater from switch inside. If it has cut-out switch in plastic sleeve attached, be sure to check for power on both ends of that cut-out switch. If power only in but not out, replace it. As I said,that brown wire comes from switch, so if no power to it, check at switch. The other brown wire goes back to connector on ignition board. If power is there, turn switch off, take an eraser on end of a pencil and rub contacts on ignition board/module to clean them off, as well as spray electrical cleaner on contacts of connector to make sure you have a good connection. Check all ground connections as well, and if you have 12 volts at brown wire to connector on ignition board but still no spark, replace ignition board/module.

Are you getting any hot water from taps? If not, check by-pass valve on back for proper positioning. You want cold going in bottom fitting open, as well as hot coming from top fitting open too. Any valves etc., in between should be closed. Let me know what happens please.

The two switches control the water heater either in the gas or electric mode. The switch with the lights would be for the gas operation, and the switch without lights would be for the electric mode. Prior to operating either switch, make sure the water tank is full of water. Turn your hot water tap on, if water comes out, tank is full. Connect trailer to 110 Volt source, turn circuit breakers on, Place switch without lights to on position. If water does not heat in 45 minutes, Install new heat proble. The gas mode should be repaired by someone that is familiar with that system. Atwood can provide you with a local service center.

It usually only lights when starting up on propane, or if it didn't ignite for one reason or another. Usually light off indicates working o.k. Are you sure the electric element hasn't been on and water is heated already? Carefully open pressure relief valve slightly and see if water is hot or cold.

On gas, usually it may light momentarily when first igniting, but as long as it lights on propane, the light goes out. Only if there is a problem that cause it not to light, will it stay on.

CLEAN THE CONNECTIONS AT THE CIRCUIT BOARD WITH A PENCIL ERASER. MAKE SURE U HAVE 12V POWER TO BOARD. IF AFTER CLEANING AND THERE IS POWER, BOARD IS BAD.

there is a big diffrence between a gas and an electric water heaters,, what you have on here is a 6 gallon water heater, it will take longer for electric to keep up hot water then it would for a gas water heater,,