I would guess that the fresh water tank did not fill up because the drain valve was open, and whatever water leaked in from the fill valve being in not quite the right spot just drained out more or less immediately. It sounds as though you took the proper corrective action, i.e. adjusting the fill valve.
Has the water heater worked previously? If you've used it in the past, one thing I would check to begin with is that the bypass valves are set properly for water heater operation and not (partly) bypassing it. Checking that there is water in the tank (by, say, operating the relief valve and seeing if water comes out) and whether it's getting hot would help. If the propane heating turned off after a few minutes, it could be because the water in the tank was hot but it just wasn't getting out. It could conceivably also behave similarly if there was no water in the tank, in which case the 120V element is probably now shot and needs replacement, and possibly some of the gas safety overheat gizmos also need replacement.
If it's not bypassed and has water, then it's a matter of troubleshooting the heater controls etc. as Old-Biscuit wrote about.
