Chevy Silverado 14 fans run high speed ac don’t work

Possible bad fuse, relay or switch.

The engine cooling fan system consists of 2 electrical cooling fans and 3 fan relays. The relays are arranged in a series/parallel configuration that allows the powertrain control module (PCM) to operate both fans together at low or high speeds. The cooling fans and fan relays receive battery positive voltage from the underhood fuse block.
During low speed operation, the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. This energizes the low speed fan relay coil, closes the relay contacts, and supplies battery positive voltage from the low fan fuse through the cooling fan motor supply voltage circuit to the left cooling fan. The ground path for the left cooling fan is through the cooling fan s/p relay and the right cooling fan. The result is a series circuit with both fans running at low speed.
During high speed operation the PCM supplies the ground path for the low speed fan relay through the low speed cooling fan relay control circuit. After a 3 second delay, the PCM supplies a ground path for the high speed fan relay and the cooling fan s/p relay through the high speed cooling fan relay control circuit. This energizes the cooling fan s/p relay coil, closes the relay contacts, and provides a ground path for the left cooling fan. At the same time the high speed fan relay coil is energized closing the relay contacts and provides battery positive voltage from the high fan fuse on the cooling fan motor supply voltage circuit to the right cooling fan. During high speed fan operation, both engine cooling fans have there own ground path. The result is a parallel circuit with both fans running at high speed.
Your best bet would be to take your vehicle to a qualified repair shop !
Relay Driven Dual Cooling Fan Diagnostics

I'm going to assume you have the manual control version. The relay in the resistor allows the fan to run on high and bypass the resistor circuits. There is a 40amp blower fuse for high speed and a 30amp fuse for the other speeds. The motor is grounded thru the resistor.
Do you have power and ground at the motor on any of the settings ? ?

I passed this question the first time I read it, so I will take a stab at it now.
The fans don't come on until the compressor has pumped the freon pressure up to say 150 or 200 psi. And the compressor clutch has to have voltage to engage the clutch.
I wonder if the clutch is going and needs 14 volts instead of 12 to engage ? Or the relay that powers the clutch ?
Speeding up the engine would increase voltage from the alternator.
This is assuming the serpentine belt is tight and everything else is working correctly.
I think I would swap the relay with another and put a meter on that circuit to the ac clutch to see what it takes to engage it.

you probably need new control switch.

Low fan speeds go thru the ignition switch - only the high speed is directly connected to the fan motor. ?so to fix that dilemma you need a new ignition switch. Could also be the source of your other issues.

there could be partial contact in the blower controls which has resulted in total loss of contact, in blower speed affected. replacement of the entire blower control switch should resolve it

Run 12V directly to the motor and see if it will run, if it dosent than the motor is bad, if it does than the resister is bad, the resister makes the blower run and also regulates the speeds for the blower, but chanses are if it was making a high pitch squeel before it quit the motor went out.

you need a resister found under your air duct by the passenger floor under dash board auto zone sells these for about 25.00 you may as well buy cabin air filters while your at it . 1 of the screws will be a pain to install back into the duct work I left mine out didn,t make a difference . you might have to order it as they are a comman item oh you will need a vacuum to clean up mess from cabin air filters .this is not a hard job .

If it is working at all then the relay and fuse is good and the problem is either the little vacuum hose on the back of the control switch panel or the panel itself.