By TEMPORARILY shorting the pressure switch leads at the furnace, you eliminate or confirm a pressure switch problem. If there is no change in random "no start" behavior for the furnace, then you know the pressure switch is not the problem.
You need to determine what type of safety sensor or switches are in the field control unit. I would assume there is something to tell the furnace that unit is operating correctly.
You say the power vent was replaced to solve this problem. Was there a previous power vent. If so, did the furnace work correctly with this previous vent?