Let me run down what Im thinking.... maybe something there will help...

1) Press LIGHT on gas controller, allows gas to flow to the pilot light but only as long as the button is pushed

2) Light pilot, keep button pressed long enough the thermocoupler gets hot, which keeps the gas flowing to the
pilot light (when something goes wrong, like low gas pressure or pilot gets blown out, the thermocoupler gets cold
and shuts off gas to the pilot light)

4) Thermostat: This controls when the furnace "comes on". If temp drops a few degrees below the set temp,
the furnace comes on and runs until its just a few degrees above the set temp... or right "at it".

The thermostat should do two thing:
1) Cut on blower fan to force hot air
2) Cut on main gas on the gas controller to get fire on the flame rails

Im thinking a few things may be wrong
* gas controller is bad
* bad wires
* bad thermostat
* no power to the thermostat (bad wire, blown fuse, tripped breaker, bad battery, low voltage, etc..)

Again, I wish I were closer so I could help...
EB