Most residential swamp coolers dont have a capacitor unless it's a one horse motor. The window units dont run any motor larger than 1/2 horse.
The only way that motor has a capacitor, and it's rare, is if it has a three speed motor. Adobe air (whisper cool) came back with a three speed motor option on one of its window models many years back and if that is your situation, you will have to repair the motor you have, or put a two speed motor in its place.
Make sure you dont have a blower bearing trying to seize up on you, if not then its probably the motor.