Since the furnaces are auto ignition models you may want to test the sparker?? It should be a L shaped probe with a ceramic insulator that is ner the burner. If the gap is too great or there is some rust shorting it out it will not work.
Also you mention that the fan blows but the heat does not come. This could be a bad Sail switch that is not sensing the air pressure in the ductwork and so it will not let the furnace light. Try closing off with the louvers on a couple of ducts and see if the additional back pressure gets it to light.
The logic on most furnaces ignition procedure:
1. Start fan
2. Sense Air pressure Via the sail switch.
3. Open Gas Valve
4. Fire ignition for 5-10 seconds.
4A. If furnace lights, run until demand for heat stops or thermocouple indicates no flame.
4B.If furnace does not light, Shutdown igniton for time out period and retry starting at #2.
After three tries the logic usally stops trying to light and will require a restart from the thermostat.
Hope this points you in the right direction. Remember playing with fire (LP) can be dangerous!