My furnace is not kicking on. It is a York model 44CF22-B. Is there something I can check before I call a repair service in?

https://www.york.com/residential-equipment/heating-and-cooling/gas-furnaces

That's an older YORK product. The serial numbers are all coded by the alphabet. York or Luxaire parts house can help you. Probably about a 1980's unit. Hope this helps!

The "mother board" or integrated control module is essentially the brain that controls the sequence of operation in your gas fired furnace. It is located, generally, in the blower compartment. That is the bottom of the two compartments of the in the furnace. It looks like a circuit board with all the wires of the furnace leading to it.

Probably the flame sensor is dirty. Should be wire protruding into flames opposite end of flame tubes from igniter. Clean with steel wool.

Check for a short in the red and white wires.

Check pressure switch for inducer motor. If switch closes, check for crack in ignitor. If gas valve opens and you can hear/smell gas, the ignitor is bad probably. If pressure switch isn't closed you need to check for blocked vent/chimney/heatexchangers.

I had the identical problem with my York. Problem was the burners. The heating element would light the first burner but the flame wouldn't move to the other burners. The flame sensor didn't detect a flame on the last burner so the gas valve would shut off. I removed and cleaned the burners then reversed the first and last.

Have your gas supplier verify delivery pressure. Too high or low, the valve will lock up. Should be a free service.

Your fan delay relay has failed and must be replaced.

On is just the blower fan nothing else, check to see if there is a reset button in the tstat or tripped over load inside the furnace, inside the furance is some safetys, you will see wires runing from each other and finaly to the gas valve, push each untill one of them clicks,then your furnace should start back working, but I would still have someone come out and check why it tripped, because as I said it is a safety, and when it tripps it is for a reason.