First let me say that I worked with my father when I was a teenager, and learned quite a bit about furnaces. He was a serviceman for a gas company. My experience with him gives me confidence to delve into this type of problem, but if you do not have such experience, then it's best left to professionals.
I had the same symptoms with my furnace, so I removed it from it's undercounter location and disassembled it. I found that a small insect(probably a spider) had plugged the orifice which feeds the gas into the burner venturi. At least it was plugged enough to limit the gas flow which prevented the ignition of the burner. All else was normal, spark, valve, etc. After cleaning the orifice (jet) or spud as my dad used to call it, it worked fine.
I found a solution to this recurring problem by placing a fine screen over the vent through to the outside of the camper. This has prevented insects from entering the burner from the outside, and I haven't had any trouble since.
I'm not recommending anyone do this repair. Only those with experience with gas appliances. Care must be taken to ensure no leaks after reassembly.
Tom & Carol