I have a Goodman GMP-100, purchased in 1996. Never a problem over the years but last year I had to replace the flame sensor. A $5.00 part, NO PROBLEM! Over the last couple months I notice when the thermostat (digital/programmable type) was in the OFF position, the exhaust fan would come on, then the large blower motor would come on but no flame or A/C condenser. Both fans would run for a couple minutes then shut off. This cycle may occur once or a few times in a row. I replaced the thermostat with a Hunter Electronic/Mechanical Thermostat, Model 40135. I don't recall the fans coming but now it is starting to happen again even with the new thermostat in the off position. Owners manual for thermostat says if system continues to operate when the thermostat is in the off position, replace unit. It has only been installed for about a month. Any suggestions?

To me it sounds like you have a slight 24v short in the system and its putting the control board into test mode.