'84 300ZX AC compressor

Just took my recently purchased 1984 Nissan 300ZX to a Firestone dealer to replace the starter. That went well, though Ithe 300 bucks wiped out my grocery money.

Now the AC worked when I took it in on Saturday, but now it blows the same temperature as the vent and I don’t hear the compressor noise nor notice the telltale change in engine speed on the tachometer.

What did they do?? Are there any relays or fuses I can check before I resign myself to a life without air??

Odds are they did nothing because of the starter repair.
A look at the schematic shows there are 2 10 amp fuses for the compressor relay. One is the main power source and the other is the trigger.

The relay shows 4 wires; blue trigger wire, sky blue main power lead, yellow/red to the low pressure switch (part of the trigger circuit), and the yellow/green which powers the compressor clutch.
Take a short length of wire and jump from the yellow/red lead at the relay to a ground somewhere. Anything metal on the chassis or engine will do. If you hear the air compressor engage then odds are the refrigerant is low due to a leak and the low pressure switch is not closing.

Since you just bought the car and it’s the first of summer, it’s not unheard of for a seller (individual or dealer) to try and make sure the A/C is cold by charging it up.
With a leak this charge may last a month, week, or barely a day.
Some sellers may not know that doing this is a temporary fix and others know full well that it’s purely a stop-gap measure to get rid of the car.
Hope some of that helps.

(And I should add in regards to the jumper wire, do NOT leave it like this to try and make the compressor run. This can lead to a destroyed compressor.)