The fan coming on indicates you have no issues with the temp sensor, etc. There is a call for heat and the fan is responding. If the fan is running the logical next step is the vacuum switch would close and the ignitor would glow. Take it from there. When the fan kicks on, do you hear an audible click of the gas valve after a few seconds? If so, that will tell you where to go next. A click means you are actually getting the valve to open and the problem may lie in a plugged burner of a fan turning too fast. Too fast will suck the gas off the ignitor. If there is no click, ensure the fan tube is not chewed by rodents. You can remove the two screws on the vent plate and then pop the corners on the top to lift off the top. If the tube has a hole in it, the vacuum switch can't close and call for ignition. If the tube is good, the next step is the vacuum switch itself. It may be stuck open. Bypass it, restart the heater and see if it fires. Any of these obvious items not working should result in a call to a tech to fully test the heater. Items such as a weak ignitor, bad ground, poor gas pressure, etc should be checked.

Of course, before all of the above, make sure the gas is ON. The part mentioned about the fan spinning too fast is noteworthy. Have you had the fan replaced recently? Maybe it was the wrong part number. A quick test for any NT doing this is to power the heat down, cover half of the vent with a brick or toolbox and fire it off. What you will do is restrict the exhaust potential of the fan and keep the gas on the ignitor. If it fires, clear the vent and replace the fan assembly. They will periodically wear to a point of spinning too fast.