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I tried touching the red and white wiring together and it don't come on light it should, but if you put a AA battery between the wires, the burner comes on.
Never heard or doing that, but if that works it means that the battery is providing current to the relay that turns the furnace on. To me that indicates that there is a problem with the transformer that normally provides low voltage current to the thermostat and subsequently to the relay. Suggest you check transformer for high voltage in and low voltage out. Also check low voltage wiring at transformer.