Sounds like either the capacitor or the connections to the capacitor have burned out. Parts really aren't too expensive. Maybe $50 at most. Labor is going to get you for between $250-$500 though
That's the most common problem, especially if the unit has some age on it. Also, blown capacitors are often the sign of other problems, like low coolant, which stresses the motor.
If you have a multi-tester you can figure out where the break is. Word of advice, though - make sure you ground that capacitor before you touch it. If it's not the problem and still has a charge, it will hurt like a mutha.