So the dash a/c will not blow cold, this tells me the fans are working so the switch must be ok. Now to not blow cold either the compressor is not coming on or the freon charge in your system is not correct.
With the a/c switch on and temp to full cold it the compressor turning (clutch engaged) is so the bet is your freon is now, means you have a leak somewhere. If the compressor is not running, the switch is not getting the power (12V) to the compressor clutch. Check fuses and relays in system. Don't know why you would need a diagram of wiring as everything on the boards are labeled. Find another shop that can spell A/C.