coolant won't have anything to do with it,
Turn on your ac and see if the fans are on. they should come on within a few minutes.
If they don't come on, theres your problem.
Also, look at the AC compressor, the pulley spins separate from the clutch. See if the clutch is engaging at all.
If its NOT engaging, check for power/ground. No power, Check fuses or pressure switch
If you do have power it could be a bad compressor.
If the clutch is engaging on/off very fast, it could be low refrigerant.
The ac compressor clutch will not engage if the refrigerant is too low.
Check for oily spots on your ac condenser, quite often, a rock will puncture it and you'll loose all your refrigerant,
Best thing to do is to take it to a shop (independent/trusted of course) that does AC. have them evacuate it and recharge it. that will tell you how much was in there.
If you need help troubleshooting, keep the questions coming. I specialize in AC systems
i can go into detail about any of the things i said above if you need help.