Cooling system

I was driving the A/C turned off and when I came to a stop the car stalled. I restarted the car and drove without A/C. It would not work. Next time I turned it on it made a rattling sound. As if something like a hard plastic was stuck close to the fan. I took it to the near auto shop and they told me that I needed to replace the whole cooling system because the clutch was loose. Is that right? Could I just replace the clutch? Does having a loose clutch cause the A/C not to work? If the A/C doesn't work and they didn't find a leak means that I have to replace everything?
Audi 2002, A4 Quattro, 1.8T, 98K