There are no brushes on these motors. Brushes are used on DC or AC/DC motors like those for vacuum cleaners, shop vacs, blenders, electric drills, etc. The pump motor does however have a centrifugal switch for the starting winding. Switch opens when up to speed. Since this motor isn't making any noise or hum at all, sounds like a completely open circuit. Could be the thermal breaker opened and won't close again or a wire blew open somewhere. When you have the motor off, try running it without the pump stuff attached. See if it makes any noise at all. You can also do a continuity check of the breaker, windings, switch, if you have an ohm meter. Wish I could offer more advice.
Al