From your description it sounds like a stuck blend door. The mode selector sounds like it's okay as you can send air out the floor, dash and defrost. The cold lines should mean the actual A/C system is working, you just are not getting the cold air through the HVAC doors. On that truck it should be a manual cable control for hot and cold. However it isn't fun to get at the cable on the door end, you have to remove the dash to get to the clip that holds the cable to the door crank.
However you might want to pull the heater control out first just to make sure that the cable didn't fail on that end first. To do that you remove the dash trim then the 4 screws that hold the control in place. Then pull the control out and you should see the clip that holds the cable in place. Try moving the control and see if the cable moves. If it does the other end has either broken or more common it has slid in the clip.
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Wednesday, May 19th, 2021 AT 9:53 AM