A/C not working after a tool rolled down and contacted both battery posts

Dear sirs,I had been working on my car changing the timing belt,water pump and belts.While finishing up and topping up water one of my tools rolled off the top of the motor and contacted both battery posts and shorted it for a split second.This where my problem lies I think? The A/C wouldn't come on.I checked the low pressure charge,it was too low,I charged it up.I checked the relay first,took cover off relay and found the contacts black and burnt.So I replaced it.Still nothing.I then checked power at fuse block .Power is there.I checked the condenser fan ,it works but doesn't come on automatically. Controls in the cabin and fan motor work fine.The car will not blow cold air!The big question does the PCM of my car control any functions of my A/C system?Did it get damaged when I shorted the battery?The car except of A/C works just fine.I cannot fine an answer whether the PCM controls my A/C on the internet any where! Please help if you can. PS, your videos are the best on all of YouTube!! Thank you so very much, Paul Taylor