Chi
Your house it cold, your furnace cycles on blows cold air and stops. The process is repeated endlessly. Those can be the symptoms of two different failures. These symptoms indicate that you have a dead main board or a failed hot surface ignitor. Replacing the main control board will cost well over $200 just for the part. The good news is that far more often the failure is caused by a broken hot surface ignitor.
If it is a failed hot surface ignitor the fix is fairly easy and relatively inexpensive. The price of the part will vary from model to model. The one for my furnace costs about $30 at the supply house. The common "off the truck" price from a HVAC repair person will be about double the price at the supply house. With a normal trip charge the price to have this repaired in my area by an HVAC person is 140-200 dollars. Labor rates vary widely across the country so your mileage may vary.
You need to understand the boot sequence for a modern furnace that uses a surface ignitor in order to identify the problem. When the thermostat calls for heat the draft induction fan cycles on to start blowing air up the vent stack. Thirty seconds or so later power is supplied to the surface ignitor. After a defined period of time it is glowing red and the gas valve opens. The glowing hot surface ignites the gas and the ignitor powers down. If the ignitor fails to ignite the gas the gas valve closes and the furnace runs for a few minutes to purge the gas from the home.
We have filmed and uploaded a video of the boot sequence described above to youtube. Watch it here.
Now that you understand what should be happening, identifying a failed ignitor is a fairly easy process. Remove the access panel from the furnace. Watch it try to cycle one time. If the ignitor does not glow red then examine it closely with a flashlight. More than likely you will be able to see a darker spot usually near the center and perhaps you will be able to see the break.
The absolute best way to always get the correct part is write down the brand and model of your furnace and always take the old part with you to the supply house. The ignitors wary little in style or function but there may be significant differences in the plug that attaches to the control board or wiring harness.
Turn off the power to the furnace and remove the ignitor and mounting plate. If this is your first time or even if it not, I suggest you leave the ignitor attached to the mounting plate because it is easy to forget which way it mounts in the time it takes to visit the supply house and drive back home.
In an emergency you can always use a universal model and splice the wires. I suggest you avoid that if at all possible as these wire are covered high temperature insulation and subject to a lot of heat. If you must splice keep it as far from the burner as you can and use high temperature wire nuts.
Never touch the silicon-carbide, "hot surface" part of the new ignitor with your bare hands or any other body part. The oil from your skin can create hot spots and lead to a premature failure of the ignitor. Cheap, cotton, jersey style gloves or any other clean well fitting glove should be worn while installing the part in the furnace.
The replacement on most units only requires the removal of one or two screws to remove the unit and mounting plate from the furnace. Then one additional screw must be removed to detach the ceramic base from the mounting plate.
Attach the new ignitor to the base plate then return it to the furnace, tighten the screws, plug it into the cable or control board and you are done. The silicone-carbide finger will break easily if dropped or bumped. Restore power and you should be good to glow.
I suggest you save the box or part number for next time. These things have a very finite life span. Or better yet why not buy two and keep a spare on hand for next time.