Diagnosis would go like this:
- 120VAC present at terminals labeled 120 and NEUT?
- 24VAC present at TH and TR? (thermostat calling for heat?)
- When calling for heat is 120V present at IGN terminals AND HSI not glowing? (if yes replace HSI, if no suspect large relay)
- HSI Glows and 24VAC present between VALVE and GND? (if yes, suspect gas valve / safety switches/wiring, if no suspect outer small relay)
- Failing all that test the inner small relay, inspect all solder joints for failure and caps for leakage. (if you can't find anything at this point consider replacing the control.)
- The fan/limit control won't come apart easily.
- Typical setting are ~100 fan off, ~120 fan on, ~180 high limit.
- You shouldn't be bouncing off the high limit, if you are you have an airflow problem, oversized furnace, etc.
- Flame sense is through the ignitor.