I have a Carrier central air and furnace model 28GS 036 000. This problem began with turning the furnace on for the first time this season.

With the thermostat off and the fan set to auto. The blower motor keeps running. Adjusting the temperature on the thermostat and selecting cool or heat does result in the AC and furnace turning on, respectively, so at least that much of the thermostat is working. Disconnecting the limit control (brown and red wires) does not turn the blower off. I can turn the blower off by turning off the "blower door switch" (name given the switch on the wiring diagram) at the furnace, but turning off this switch prevents the burners from igniting. Everything worked fine in summer (AC and blower), so obviously something is broken.

Hi,
I would call a heating/air conditioning repair person. It could be a solenoid switch on the motor, gone bad, and not allowing the switch to shut off automatically.
My own heat pump (both ac and heat) would not go through its defrost cycle, at the start of last winter. My heat pump repair person found a bad solenoid switch, replaced it, and now the defrost cycle works fine.

It is likely a simple matter of the relay that controls the fan is stuck. That used to be a fairly simple matter to fix, but on the newer furnaces the relay is on a control board and much more difficult diagnose and replace. The whole board can easily be replaced if you very carefully note where all the wires go. Unfortunately, they cost an arm and a leg. If that is where the relay is, replacing the board will fix the problem even if it is something other than the relay. Calling a professional could add $100 in labor to what may take a half hour.

A dealer for your furnace should have the board. If not, running the furnace as it is, shouldn't hurt anything while waiting for one ordered on line.

Shuting off the blower door switch kills all the power to the furnace protecting you while servicing the filters. Makes diagnosing problems harder too.

Thanks labman. Finally got around to fixing it. Installed a new board bought from the internet. $100 cheaper for the part then from the local dealers. Took two hours. Took my time, because I've destroyed too many things rushing. Works beautifully.