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Ok, if the fan runs but the burner won't fire up then the flue/exhaust could be blocked. It's also possible that you have a faulty draft pressure switch. The draft switch has to prove that there is adequate draft before the burner will fire up. Also check the small hose that connects the switch (top left) to the exhaust. If the hose is disconnected or falling apart that could also be the cause of the burner not firing.
No you can't jump out the switch because the board tests for that and it won't fire up if it's jumped. Yes you should get an error but since you aren't this is the most likely culprit if you aren't getting an arc from the ignitor electrodes. If you are getting an arc you should hear a ticking noise. You can check for power to the electrodes as well.
You can test the switch by checking continuity across the NO terminal when the fan is running. Remove the leads so you don't overload your meter
Sounds like a bad switch if you have no continuity across C & NO with the fan running and the vent clear. So if you want to confirm a bad switch then you need to put a manometer on the exhaust with the fan running to confirm adequate draft. Or you can just replace the switch which is a lot cheaper than buying a manometer if you don't have one. It's not that I'm not concerned about the lack of an error showing. It's just that you want to eliminate the cheap parts as potential culprits before you point the finger at an expensive control board and a switch failure is a whole lot likelier than a bad board.
You should also check to be sure the ports the vac hose connects to aren't blocked. You can poke a paper clip into the one on the fan housing not the one on the switch
The switch is calibrated to a very specific pressure. Blowing into it doesn't tell you anything. I've already said what you need to do to confirm a failed switch.
Did you check continuity across C & NO on the new switch with the fan running?
Setting high altitude parameters is a one time operation. So that's not a likely cause. So since the new switch isn't proving adequate draft your options are: first and foremost take the flue and fan apart to be sure there are no obstructions. Once you have proof there's nothing inhibiting the draft you either put a manometer on the exhaust and check the draft or you replace the fan. I had a recent case where the customer insisted the vent was clear. After considerable prodding he finally took the fan apart and found moths in the fan blades.