My furnace worked fine last Thanksgiving. Made a little trip this week and it got down into the 30's. Turned on the furnace and here is what happened: Blower turned on, I heard the burner ignite, ...
Some newer furnaces use what's called a flame sensor. This is in place to keep the furnace from feeding gas to it in the event the flame goes out. The sensor is extremely sensitive and can "foul" with carbon deposits.
They are easy to repair. All you have to do is remove the sensor and take some 600 grit sandpaper to the end of it and lightly sand off any built up carbon and reinstall it.