Your problem could be simple or complex. Let's hypothesize a simple case.
Suppose the high-tension cable that carries high voltage from the
controller, to the spark gap, is malfunctioning. A major argument against
this is that, according to you and Bubba, your action to reset the
controller by cycling the interlock switch invariably enabled the heater to
successfully operate. Yet if you were wrong on this point, then the simpler
potential faults gain new life.
Consider that your spark cable could be arcing to
ground...intermittently...perhaps based on proximity of the cable to a sharp
metal chassis edge...or even proximity of the cable to the flame sensor
wire. Thus the spark would not occur at the pilot site, the flame sensor
would disallow main burners to be fueled, etc.
You might have an overtemp sensor, or undertemp sensor, that is putting your
controller into a lock-out state.

You DID say that your repairman replace the controller, right? You ARE
presently using a new controller, right?

"Bruce" wrote in message
7.136...
"John B" wrote in :

Does your unit have electronic ignition? Do you hear interminable
sparking?

Yes, and no, in that order.

The furnace is in the garage. I'm always down there, esp. on cold
evenings, so I do notice that when the ignitor comes on, the gas flows,
and
the burners light. No problem there.