why isn't my A/C blowing cold

Check the compressor relay and also check it to make sure the refrigerant has pressure and isn't leaking somewhere. You can also visually look at the compressor and make sure the clutch is engaged.

i have a 2009 Hyundai Sonata 4 door Gls 2.4L sedan. and when my A/C went out i tried a bunch of things. I recommend looking up how your a/c works. so what i did is i looked at when i put new refrigerant in the low side port where does it go from there and so on etc... what i found is that a/c problems with Hyundai sonatas like my 2009 is at 2 places. the expansion valve, which only cost like 20 to 40 bucks. or the A/C control valve that is inside the A/C compressor. Just like you i could also see my compressor kicking on and yet nothing was getting compressed. so i new it was something to do with the compressor. dont let anybody tell you that you need to change the entire compressor, because you dont. i was told, and quoted by many different auto repair shops that i should change the compressor only costing $730 bucks! but i didn't listen and i figured it out myself and changed the control valve within the compressor for only 40 bucks or less. the expansion valve and the control valve ordered from " Rockauto.com" good luck.