When people drive around with dead fan(s), and it is easy to do on the diesels since they don't need much engine cooling at slow speeds anyway, the compressors often suffer.
Neglected cabin filters will also allow buildup of debris on the evaporator, which will significantly impact both airflow and heat exchange.
Just a quick thing to check, and this is my quick seat-of-the-pants method to make sure the system at least works component wise: Start the engine, switch the A/C on, and get out and walk around to the side/front of the car and put your hand on the low side line*. It should be obviously cooler than ambient, and should be getting cooler by the second, cold enough like it is an aluminum soft drink can just taken out of the refrigerator. And assuming the engine is cold (just started), the fans should be pulling some warm air across them that you can easily tell is warmer than ambient.
If both those happen, you at least know the system as a whole is working and functional. From there, you can evaluate things like HVAC controls, airflow inside, etc. You can also raise the RPM some, and the compressor should still stay engaged... and if it is warm enough out, the fans may ramp up to high speed. If the clutch cuts off, or the fans remain on low speed despite it being hot out, the system is possibly low on charge, and then you can get into the gauges and such.
*low side line is the FAT one, that goes to the compressor inlet from the expansion valve. The other line gets HOT, so make sure you know and understand which is which before you start feeling things.