A/C compressor does not kick on

Hello, when a temperature sensor reads -40 degrees it means that the sensor has an open wire inside of it or a wire going to the sensor is open (broken). The -40 degrees is a default strategy the cars computer reverts to. Here is 2 wiring diagrams of the A/C wiring, there isn't much involved. Just the relay you already checked and the wiring the computer. There should be a code stored in the computer for the ambient temperature sensor. So you need to have the computer scanned for codes to start with, your local parts store will scan it for free. You should check Fuse #59 it feeds the A/C compressor relay. You can also check at the compressor for power on the light blue wire with the system on. The relay is directly controlled by the cars computer. It sounds like because the computer is seeing -40 degrees outside, its probably not turning the A/C compressor on. But I would address the temp sensor first, then see if your compressor turns on. Has the check engine light been on at all?

Yes you can reconnect the 2 wires as long as they're the same color, just so you don't attach the wrong wires together. Are you getting codes for the 02 sensor as well?

Okay, so we have to figure out which temperature sensor has the broken wire. There's an outside temperature sensor and an Evaporator temperature sensors. One has a brown wire and the other is brown/white. The yellow and green wire is ground for both sensors. If the Evap temperature sensor wire (brown) is broken it will not allow the compressor to come on.

Just go by if it's a brown wire or if it's a brown with a white strip, it's located behind the front bumper. The outside temperature sensor is like any other thermistor, same as a coolant sensor, intake air temperature sensor. It receives a 5 volt reference and the ECM monitors the voltage on the circuit to make calculations. Never apply 12 volts to it. You may have damaged the sensing circuit in the climate control unit.

There may be other damaged wires too, depending on how that one got broken. I would follow that wire as far as you can and make sure there's no other damage. Here's the rear A/F sensor (02) Bank 1 Sensor 1. Check the wiring for this as well before replacing the sensor.

Yes, the A/F sensors are wide band 02 sensors and are before the catalytic converter, the 02 sensors after the cat are narrow band regular 02 sensors. Here's a diagram of the climate control unit if you want to check the brown/white wire coming straight out of it. Should have a 5 volt reference coming out. You may want to go through your fuses too, just to verify they're all okay. That broken wire hanging down could have shorted out on the frame. Check this #3 7.5amp Fuse as well, it powers up the climate control unit and panel.

The climate control unit is different than the display panel with controls on it. The Climate control unit takes commands/inputs from the display panel. Here is its location:

That's good, check the sensor unplugged for resistance on the meters ohm setting to make sure the sensor isn't open inside. Can I ask why you cut the wires to begin with? Just curious. As for your A/C problem turn the A/C on and check the wire at the compressor for power. The light blue wire.

Your meter is reading OL? If so definitely a bad sensor. Open windings inside. Need to replace that.