Can't find the circuit board of my HVAC system
You may not have a C wire. The C is a common used to provide a constant power circuit (C is the Negative or Ground) for the thermostat to use. 

In this furnace there are only 2 wires that a manual thermostat or battery operated on will connect which turn the furnace on. 

Your only option is to run another wire (Or use another if there are extras) and connect it to the negative pole on the transformer (LOW VOLTAGE SIDE). 

Its often the blue wire but I would need a better angle on the transformer to tell for sure on that particular one. 

You should also check that the output is no more than 24v. If its anything else it could damage the thermostat.  

CAUTION: There are live 110 lines into that transformer. Make sure your power is shut off at the breaker before touching anything in there. Make sure its covered when your done.