If everything you say is good is good then listen for A/C compressor next. You should hear it 'click' on when clutch engages (w/ serpentine belt) when motor running and a/c on. If not clicking on, first spot to check then is refrigerant level...
If not enough refrigerant 'charge' it will be from another issue. It's a closed system and thus leaking... i.e. condenser/radiator puncture. HVAC blower still blows anytime system is on but (as you are experiencing) only ambient air if condenser is not running.
Any half decent shop will be able to test your refrigerant level first (DIY kits are available). If it's low they will add some w/ a dye to find source of leak. Do NOT just add more refrigerant as solution b/c again it's a closed loop system which is compromised somewhere.
If enough refrigerant the next spot to check is condenser. If it has sufficient voltage but not engaging then it is the issue. If not enough voltage then look to relay and fuse (which may be blown again b/c of issue w/ condenser).
Not many places to check... Good luck
