Just thinking out loud - go start the car. Turn on the a/c (make sure its' on, sometimes when its' bright, I can't see if the light is on or off on the button), and locate the compressor.
It should cycle. The belt should always be going, but sometimes the compressor clutch will kick in, and the front face of the pulley will spin. When the clutch is out, the front face won't be spinning even while the belt is moving.
Many things can cause no cold air. Freon loss is one reason. No freon = no cooling even if everything else is right on. Easy test, I haven't looked at mine, but many A/C systems have a so-called "sight glass" near the receiver / dryer assembly. Looks like a fitting with a small circle window. You should see the occasional bubble when the clutch is in. No liquids blowing by, no bubbles, no freon.
Then, there is a pressure switch that can sense freon loss. If it detects a loss, it can keep the clutch off to keep from burning the compressor up. If that switch goes bad, the compressor won't run (my test at the beginning).
If the wiring to the switch is broken, or looks good but is corroded inside, no lockup voltage to the clutch = no cooling. If the wiring to, or the clutch is messed up, = no cooling.
Seriously, if the belt is broken = no cooling. My brothers non-Ford SUV has a dedicated A/C belt. It really was that simple.
If you have an EATC (fancy controls inside), a failure at any of several points = no cooling. If you have the basic system, if there is a vacuum loss, the flap over the evaporator in the plenum won't flap over = air, but no cold air.
BE CERTAIN before you buy one of those "I done fixed it myself" kits, that you know for a fact what refrigerant you are using. There are retrofit kits, so you think you are using one thing, but actually you are using another.
Good luck!
-Shawn
