Blower fan won't come on on the ac side, but it

Test the electrical circuits ! Manual HVAC or automatic HVAC ?
Do you know the difference ? Heater / A/C blower motor electrical control diffrent . Manual has resistors an a relay for different speeds , automatic has a blower motor control module .Free wiring diagrams here http://www.bbbind.com/free-tsb Enter vehicle info year , make , model and engine size . Under system click on HVAC ,then under subsystem HVAC controls will pop up . Click the search button , then the blue links . First off you need to know what system yours has , manual or automatic.
GMC Yukon HVAC Blower Motor Won Turn On
Blower Motor Problems Auto Repair Help

The fans heat speed is low speed and the cool speed is high speed. High speed is controlled by the fan relay normally open switch, the low speed is controlled by the temperature delay or time delay.
see diagram

they are not relays its a blower motor resistor a one piece unit usually held in by two bolts and an electrical connector either under the passenger side dash or behind glove box

it could be the relay or the winding in the motor try wiring a different speed on the motor by switching wires if that works its the motor winding

you might check your switch sounds like to me that your two lower speed sides of the switch maybe burnwed out.

Likely either a bad switch or relay. I'd also probe all fuses(regardless of what they are for) with a test light just to make sure they have power at both ends of each (takes ten minutes and eliminates the possibility that you missed something there.)

Check fuse supplying fan is not blown,
Check blower control switch is operating OK,
Check relay controlling fan is operating OK,
Check variable speed resistor pack is not faulty (the resistor pack is usually located in the blower ducting, in the blower airflow),
Check blower motor ground connection is not missing.

check the fuse in the fan-fan relay-check voltage at the terminals of the blower if you have the voltage problem is to check the blower motor of the blower speed control

Heater blower motor resister is bad, replace, located under dash above heater motor.

1. maybe your ac condenser blower is not working properly
2. slipping ac belt
3. air con compressor hub is sliding due to oil leak