Back from Vacations. Are you still having problems? if you do you need to get yourself a voltmeter and learn to use it if you are not handy with it. what is weird about this is that the voltage that comes from the battery or the converter goes to the same wire at the fuse box, so it should not matter which one is working, the voltage and amperage supply goes thru the same circuit. What can be happening is that the battery for some reason is not supplying the correct amount of voltage/amperage and the motor is not turning fast enough to trip the sail switch. That would be my first guess. You would have to check your voltage input at the furnace and compare what you get from each source. What brand/model furnace do you have?