If your battery
voltage is low the fan will come on but will not activate the air prove switch. If the air prove switch doesn't activate the gas solenoid will not pull in and you get no gas at the jet.
For most furnaces the fan has to run at 75% of full speed before the switch will activate.
First test is to see if your power buss voltage is around 12.6V. Since you mentioned that you are looking for a power converter that is probably a problem. Try running the system on a battery
charger for a quick test.