How do I identify if the air conditioner compressor of my 2004 Nissan Altima I4 2.5L was bad and needs to be replaced?

Run the engine with the ac and make sure the clutch is engaging and the fans are turning on. Usually the clutch will fail. Easy to change while it’s on the car. You tube is a good place to start. Usually a bad compressor is loud when the ac is on. It fails internally and will lock up causing mental particles to contaminate the system.

To add to nando's advice, try working backward from the compressor.

In other words, what are the symptoms of your issue? Do you just not have cold air from the vents? Or do you suspect the compressor is bad for some other reason?

Like said before, what are the symptoms? Are you not getting cold enough air blowing through? Have you changed the cabin filter? Sometimes those get clogged and can prevent cold air from coming in, you might also smell a mildew odor. Let us know