Make and model of furnace will help.
"but the ignitor does not spark"
Are you sure you have a spark type ignition and not a hot surface ignitor (HSI) that should glow white *
If you do have a spark ignition then you need to check the high voltage wire from the ignitor to the control board. It will be thick like a car spark plug wire. Check the porcelain insulator that insulates the spark electrode for any signs of cracks. If you understand electronics you should test the control box to be sure it's producing enough voltage for a 1/4" spark. Disconnect the high voltage wire from the ignitor. You should see the metal cap inside the wire insulation hood. It's just like a car spark plug wire. If possible, slide back the rubber hood over the cap exposing the metal cap.
Now with work gloves on, hold the wire on the insulated part so that the metal cap about 1/4" from the furnace frame... any part that's grounded. Have someone call for heat and see if you can see the spark from the metal cap to the furnace frame. If there's no spark either the wire is bad or the control board is bad. Let us know what you find.