In older furnaces that use pilot lights the main thing that goes bad is the thermocouple. When heated by the pilot the thermocouple holds in a magnet which allows gas to go to the burner for ignition. A gas operator solenoid is incorporated in the valve  for thermostatic operation. When the pilot goes out the magnet shuts down the gas supply. If the thermocouple is new and the pilot is lit but the gas will not ignite, then the gas valve is probably bad. OR their is no power going into it from the thermostat. The gas comes on then what happens? The temperature begins to rise in the heater but the fan does not come on yet?

  fan/limit switch

Gas valves get their operation power from several different sources. Floor furnaces work on milli-volt valves. The power to operate the gas valve is done by the pilot generator. All that is needed to regulate the floor furnace is a simple 2 wire thermostat mounted on the wall in the hall.

Central air furnaces use a 24 volt valve. The wall thermostat has to rely on a transformer

 

   typical low voltage

   24 volt transformer

to power up the operator on the gas valve.

 

Newer furnaces use an electric igniter to light the flames, a sensor will detect the flame and all will be well. When the heat rises in these furnaces an electronic control board relay throws the fan on after a few moments and you have warm air coming out of the vents. If the fan fails to come on then a series of rollout switchs are mounted around the heat chamber. One above near the stack one on each side and one below the burners.They will pop out if cobwebs are in the stack or wasps nest or bird nest.Just push the button back in after clearing out the obstruction. Sometimes rusty burners will cause flame rollout too! It is very important to wire brush the burners and vacuum the debree out of the burner chamber