'02 Silverado a/c problem
 

My a/c blows cold but it blows through the defrost vents and not the vents towards the cab.....

Mode Actuator is bad. Common issue.

Yup, I agree with acnas.

Pop the actuator off and move the door manually with your fingers to double check that the door works good, then replace the actuator. Make sure to have the actuator installed and screwed down before energizing it to see if it works. In other words, completely screw down the actuator before you key on! The actuator goes through and measures its travel. If it's free floating without being connected to that door, it will never work again.

you can re-center the actuators. remove the cover, lift up the plastic drive screw from the driven gear and move the gear back to the center position. reinstall the cover and recalibrate the mode door positions.