What brand furnace do you have?
Does the pilot you have light with a small hot surface ignitor? ICP (the mfg) used what was called the honeywell smartvalve in a lot of its furnaces. You would know from seeing through the little windo that there is a glow then a pilot lights and then main burner.
Ok, we are getting close..the circuit board in your model is located in the blower compartment. You can see a flashing light through a small window in the blower door.
Can you look in trhe window and count the flash pattern, there should be a fault code chart on the blower dood that will interpret the flashes.
What I am doing is trying not to generalize the issue....The Honeywell Smartvalve had many issues and was retooled various times. But I want to make sure this does not put blinders on and miss something else.
Can you check the fault code and let me know?
There are two choices....
1) The pilot assembly is defective and not sending a signal of established flame to the gas valve.
2)The Smart valve is defective. They call this a smart valve because it actually controls all of the ignition procedure. That is why there are so many wires going to it.
Its a case of is the pilot not sending the signal or the valve not recognizing it.
If a different fault occurred to shut down the burner, it would also shut down power to the smart valve, thus no pilot.
Without the proper tester (they actually made one specifically for this valve) it is a toss up. My choice would be to replace the pilot assembly first.