Will my AC motor run if the capacitor is bad?

No, an air conditioning compressor or blower motor will generally not run properly if its dedicated run or start capacitor is completely bad or dead. Capacitors act as essential electrical fuel tanks that provide the critical phase shift and voltage boost required to give AC compressor and fan motors the torque they need to start spinning from a dead stop. If the capacitor fails, the motor cannot overcome rotational inertia; instead of starting, it will draw excessive electrical current, emit a loud humming or buzzing sound, and quickly overheat until its internal thermal overload protector trips or the circuit breaker blows. You can troubleshoot by turning off power and testing the capacitor. You can verify that the motor is safe when replacing a dead capacitor restores instant, quiet motor startup.