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When it does light the burners how long do they stay on and when they go off how long do they stay off before it lights them again?
Also this furnace was re engineered a bunch of times as it was one of the first automatic ignition systems out there back in 1985. Does it have a fan limit relay on this particular unit it looks like this....
oh, I misunderstood sorry. If you can manually pull in the pressure switch and it works then we know it is in the exhaust system.
Did you clean the barb on the inducer housing where the tube hooks up?
Take the vent pipe off the top of the furnace and see if the furnace stays on. If it does then the vent is restricted. If it doesn't work still then we know it is either the inducer draft motor not running at the proper RPM to pull in suction or the pressure switch itself but you said you changed the switch already.