Sounds like the contactor is stuck in the outside unit. Turn off the breaker or safety switch, remove the cover, and tap on the body of the contactor with a hammer handle or similar tool. If a click is heard you may have dislodged it and it may work for either a short time or indefinitely. (yeah ,I know that's kinda vague) Test it. If that doesn't clear it up, disconnect the thermostat wires just to make sure and re-test. If the compressor starts without the thermostat connected, you will need to replace the contactor. If you feel real handy, you could perhaps remove the cover, seperate the contacts with a screwdriver, dress the contacts with an emery board until smooth and shiny, and try again.