2003 chevy silverado air does not blow through vents. Condenser works. Pipes are cold. Fan works. Modular (next to fan) repalced to get fan to work. Heater air conditioner controls under radio replaced. Fuses checked seem OK.

A fan heater is a fan blowing over a bank of electrical elements, or in many cars, hot coolant water is directed through pipes in the heater assembly, in place of electric elements.
In any case, if fan is still running when heater is turned off, the source of the heat will be gone, so blowing only cold air.

Check and see if there is any Ice on the copper line that runs from condenser (outside unit) to air handler (inside) if so you need a charge. You can also make sure the fan is working on the condenser unit outside it should spin when you have the air on. If it is not you have a bad fan motor. there are other things it could be but these you can see.

you have a bad connection at the blower motor - something

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the problem is not the compressor but the head pressure is to high and the high pressure switch is shutting it off
You say really cold while driving but on/off when stationary
That indicates that the fan in front of the condenser is not working and the high pressure gas is not converting back to liquid
2 possible items to check
fan--fan relay fan relay fuse
and excessive gas in the system
take it to an accredited ac specialist shop and have the pressures checked
At this point I am thinking excessive gas

could be a leaking servo pipe. if it is knob turn type. motor failing on electric type. or a warn linc on vent control. very hard to find out you need to get your hand round the back and feel for the motor/s. on electric type. knob type with engine off move the vent control should hear a hissssing sound if no hissing sound then it is leaking.

Have you radiator clutch fan check out, sounds like its bad, air blows through radiator and a/c condenser while driving and no air blows through at stops, will cause a/c pressure to go up and not cool.

There is a flap in the venting that can stick. This vent is contolled by a vacuum operated actuator that may be leaking. This actuator has a vacuum hose that runs to the contol panel. Check the vaccum lines hear as well.

Question: You do not have leak of Freon 134A "When you drive on the road enfria.Prueba in your house and throw water with the car wash hose to pour water condenser is in front of the radiator if that way you notice that you have cooled to check the fan that cools the condenser

First check fuses, then test blower motor, Last Temp control switch

need a new AC computer