Hard to say. LP gas detectors are notoriously flakey.
Check the battery level some other way. If the lights light, the fantastic fan runs, the water pump pumps, and the stereo works then your problem may be a combination of air in the propane lines so the furnace won't light without a lot of cycling combined with a bad propane detector. Or maybe the furnace is bad, with a clogged venturi, bad circuit board, or mispositioned ignitor.
Otherwise if the water pump, lights etc are dim then the converter isn't doing it's job. Be sure the converter is plugged in and the breaker for it is on before proceeding on to more involved checks.