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So you checked where the vent terminates and it's not blocked? If so you could have a bad switch or a weak fan. You probably wouldn't feel the draft since it's very low pressure. Did you check the port where the hose connects to the furnace? You can poke a paper clip in there (not the switch side) to try and clear a blockage there.
Just clear out that port and check the exhaust vent before the start of the heating season since insects even birds often build nests in a seasonally unused vent. And of course change the filter regularly