There is no electric or vacuum fuel tap. The PGM does not stop fuel getting to the carbs from the tank, or from the carbs into the cylinders.
The PGM does control the air correction solenoids, but this will not have a HUGE effect on things and certainly will not stop the bike from running.
Very basically, the PGM mainly makes slight changes to the fuel/air mixture at mid-range rpm. And of course is responsible for the ignition advance curve.
It sounds as though the jets are blocked or the float valves are not opening.

As a bare minimum, I would pull the carbs off, remove the float bowls, remove the slow jets, main jets and emulsion tubes and make sure that they are not dirty or blocked.
Also check that the float valves are in good condition and working properly, and check the float height.

While the carbs are off you can look down into the reeds with a torch, or push them open a bit with your fingers to get some idea of what's going on and remove them if necessary.
I doubt that the reeds are the primary reason for your engine not running, going off the fact that the engine runs with the aid of "manual" fuel injection.
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