Do you get a battery light on the dash while the car is running? are the lights dimming when the headlights come on? Check the battery terminals and make sure they are clean and if it is an open battery, check the water level is correct. Could most likely be your alternator or weak battery.
Can you turn the AC compressor under the hood by hand, maybe the compressor seized.(but then the belt would be squealing or smoking)
Also my old volvo 850 Idle control valve. IAC that got gunked up and needed cleaning once a year with brake fluid. (It controls idle when different accessories are turned on) I am not sure if the 82 Vette has one, maybe other members can pitch in on this, but this could be the issue the IAC