AC Unit Not Cutting On
The thermostat cable could have been pulled loose or broken at some point.  When the thermostat is turned on, it should supply voltage to a relay on the AC unit and that normally makes an audible "click".  Checking the voltage on the thermostat wires leading to that relay should show 24vac (alternating current).

If there is no voltage, you can check the wire for breaks along it's path.  Because it is low-voltage, it doesn't have the same rules on splices and how its run as the main electrical wiring so it can get damaged more easily.  An existing splice could have been pulled loose.