A/c compressor won't engage 2005 equinox

Rhe resistor might be bad, I know you replaced it, but things come brand new and have defects

Chevrolet did a decent job of designing the compressor setup with an easy hose interface and mount bolt locations to make working in the tight space in that sector of the engine as easy as possible.
if you are determined to change it yourself, be sure to have a copy of, and follow the owners manual exactly.

It could be a fuse or the cruise motor is bad it is located buy the driver side fire wall

You have applied 12 volts and a good ground to the compressor magnetic closing coil from the battery and it still won't close and engage conpressor? it that what you are saying? If so the magnetic closing coil is defective, you will need special tools to pull it off and replace it.

pressure sensor on condenser

As with any no-start condition, you first need to know if it is no spark or no fuel.
You could try spraying carb cleaner or starting fluid into the air cleaner hose to check for no fuel. Or pull 2 or 3 plugs and check for spark.
Also take a look at the ECM for trouble codes.
It could be anything from a plugged fuel line to the gas tank to a bad relay to a dead ECM.

That switch is a Pressure Sensor, so I would not "short it" to test it. The Sensor has 3 wires. There is no 2 wire switch. So did you check the refridgerent level? it should be 80psi or so with the engine off. also check the fuses. A/C clutch fuse, BCM HVAC fuse, Blower fuse, all in the underhood fuse box.

I'm not familiar with your car however, this sounds like a straight forward resolution. If the AC clutch or compressor has locked up or dragging badly, the extra load could damage the belt. If this is true and you don't want to repair....possibly there is way to use a shorter belt. Many cars are sold in the cold north country without AC units. Try for a belt for those versions and an idler to mount instead. Good luck, Paul

I have repolaced a couple switches on these does yours show power when you cut on but will not engage ? if so probably the set/resume switch on steering wheel

Got to be a reason for the price difference if it's quoted from the same place.