My furnace will light one burner the first time for a few seconds then go out. The second time it will light maybe 3 burners for a few seconds, then go out then the blower will come on...I replaced the flame sensor but no help.
I had the same thing happen with my furnace and I had to have the blower replaced. A very expensive lesson to learn about changing filters often.
The tech told me that if it tried to start and did not pick up on any air movement it would automatically shut off the furnace.
The lack of full air flow first burned out the blower and then I lack of the blower operating kept the furnace from firing.
As others have indicated, specify your make/model of your furnace. However, based on your short description, I'd take a look at your flame sensor. This is the same exact problem I experienced when my sensor failed (it gets covered in carbon over time). You can test it, by turning your furnace off completely (power and all), disconnect your sensor, "scrape" it with a sharp knife, but don't gouge it at all (your just scraping the black carbon off of the sensor), plug it back in, and let your furnace fire up again. Does it happen again? If not, you need a new sensor (it will likely fail in 1-2 weeks again). disclaimer: If your not at all comfortable with any of this, don't do it, and call an hvac tech.