The battery light on and the A/C does not work, is it the serpentine belt, or alternator?

Battery light came on while driving, and shortly after all indicator lights began flashing at once. Power steering seemed to go away; A/C stopped blowing cold. Immediately pulled into a repair shop. They did an oil change, new brake pads, and put in a new battery. That was yesterday. All indicator lights are off again, but battery light is still on, and A/C still does not blow cold. Is it more likely to be that I need a new alternator? Or possibly just the serpentine belt needs to be replaced to crank the A/C and get battery voltage right? How do I know if I only need the belt replaced, or if I need the whole alternator replaced? Car seems to be running fine, it just has the battery light on, and the A/C doesn't work.