I'm assuming you tried to preheat and load filament into the suspect extruder and could not? If not, I'd try that first.
Disclaimer: I'm speaking from experience with a Replicator Dual, which is similar, but not the same, so take it for what it's worth.
It's doubtful you have anything inside the cavity blocking outflow, so I'd attempt to clean the input of the cavity before I'd start unscrewing the nozzles. . Unscrewing nozzles is a job of last resort.
On my machine, the screws that hold the fans go right into the stepper motor and hold all the pieces in between. Once I have them off, I have access to the extruders.
Removed the block (heat up the head until you can safely remove it), put it back together the way you took it apart.