There's a relay/controller under the dash-- I want to say it's labeled 120 off the top of my head. You should hear/feel it click when you turn the A/C on or the fan to speed 4.
Along with a ton of other things, the solder joints in this crack and fail. The solution is to simply touch them up with some (electronics) flux and a soldering iron.
This may not be your problem (there is a three-way pressure switch that needs to be satisfied with the actual pressures of your refrigerant) but it did fix AC for me.