most problem is occur on the thermostat, some thermostat powered by the regular battery, if battery is low, when furnice called for heat, burner will not be lighting up, thermostat switch also shoule be on heat side at this season.
I think that your igniter was brocken. I had the same problem before. The furnace works but there is no heat. I spent $300CND to ask a technician to replace it. Right now, it works well.