Please describe to me what exactly happens and in what order when you turn the furnace on.
Set the thermostat for it to come on, then while standing right there at the unit, cut the power wait 30 sec and turn it back on. I need to know at what point the system fails so I can help you diagnose the problem.
I have a standing pilot with no electronic ignition.
I have a 110VAC Power switch on the outside of the furnace in a handy box.
If I turn the power off there the pilot light goes out. The transformer is Off.
Turn 120VAC back on and I can light the pilot and it stays lit. I have to manually light the pilot after the power goes off.
I just have a heat no AC.
My transformer has a blower relay on it.
Transformer terminals are C, R & G
Transformer C goes to one terminal on the Gas Valve.
The other terminal of the Gas valve goes to C on the thermostat.
R and G go directly to the thermostat.
The transformer C & R terms are labeled = Load.
If I measure voltage between R on the thermostat and either terminal of the Gas valve, I get 24VAC on both the terminals.
There are wires connected to G & C which look like they go inside the Blower relay.
I just don't quite see how the three terminals work together.
G would be the wire that sends the blower fan on if you set the thermostats fan switch from "auto" to "on". I'' refer to it as the "fan wire". They are usually but not always green.
C is the common and is usually but not always blue
If you have 24V going to the gas valve, and the coil is not bringing on the valve, then the valve is bad.
The burners should fire up, then when the heat exchanger reaches temp the blower should come on.
It does indeed sound like the GV is sticking.
Let me ask you this.... Do you have a copper gas supply line anywhere between the meter and the furnace?
Copper reacts to the chemicals in natural gas by forming an ashy, flaky substance that builds up on the interior walls of the copper. It eventually ends up clogging those gas valves after it builds up to the point of flaking off and flowing down line.
"IF" you have copper, there is a huge probability that this is the cause for the GV sticking. You will also want to make sure there is a drip leg on the gas line near the furnace to catch dirt and other dibri. (The flaky ashy substance is so light it will go right over the drip leg and clog the valve.)