my outside ac unit will not turn on

My outside unit does not turn on itself, but it does work. I just did a quick repair just thinking it was the capacitor and it was only 15 dollars for a new one so I changed that out and still had the same problem. After this I pushed in the contactor and the unit will turn on so I measured for voltage and am not receiving 24 volts to the unit. I just moved into this house so do not know what was done beforehand but we have two thermostats one controls the ac the other the heat. When I measure the voltage across R to Y, or from R to G, I receive 24V. The wiring that is connected at C and Y are going to the outside unit and I do not get any Voltage across here which in turn means it is not sending out the 24V to the AC Unit i believe. The wires connected at Y and C are going directly to the unit outside. The wires at RGY are connected to the thermostat as far as I can tell. I should mention that the fan will come on in any operation. set to on it comes right on. If in auto it will also come on (on the thermostat).