If you read across an open circuit you will read source voltage, in this case 12V. When you hook the circuit up it wont necessarily read the same. It sounds like you have a wiring issue, that is, an open, most likely on the hot side. With the compressor disconnected, read resistance from the AC amplifier hot wire to the hot side of the battery. It should read close to 0 ohms if it is supposed to be hot. Let me know what you find out, or if you want to call me you can.