A/C stopped working

Last summer when I had the alternator of this minivan replaced, the A/C stopped working right away. It started blowing out warm air only. I replaced the fuse relay. That didn’t help. I can’t really check the refrigerant level as the compressor clutch would not engage. The fans seem to work fine every time I hit the A/C button. Rpm’s also rise when I do that. The clutch is not locked as I can spin with my hands. I also noticed when I was looking under the hood that one of electrical connection wires was disconnected from the other one that I believe was attached to the A/C fan. Even after connecting that, the A/C still didn’t work fine.
I would appreciate any help on what to be doing next.
Thank you.
Aizy