Welcome to the forum,
You say it "seems" to have plenty of coolant", but how can you tell. Just a little low will make the sensor ("low pressure switch") shut down the compressor. There are plenty of air-conditioning places that will check you system for free ( thinking they can sell you coolant or parts if you need them). Yes, the low pressure switch will stop the compressor for full air or the defroster.
You say yo know about the fuse, so I take it you checked that. The LPS sits on top of the round silver canister in the back of the engine on the left side (see photo below). To see if the switch is working, pull off the electrical connection and make a jumper (paperclip) on the switch between the contacts. Start the car, turn the air on and if the compressor turn on, the switch is bad.
