Well, we will spare you a LONG discourse on your ill advised purchase!
As to the motor, that component may include a start relay AND a run capacitor. Once the motor starts, the relay, or a start capacitor, would not affect its full power. But if the capacitor functions as a run capacitor, which is what I would suspect, then the motor can overheat and/or not run at full speed or power.
And not to rub it in, but now the store has ANOTHER unit with a missing or defective part, to sell to the next unsuspecting sucker!