I bought a 1983 240D today, it has a new AC system put in (new everything) at a cost of about $950 last year. New compressor on 134, new ducts, new condenser, etc.

It worked today, and then it cut out. I noticed that when it was working, the AUX Fan was spinning but now, the AC blows only warm-to-hot air and the AUX Fan in the very front, right behind the grill no longer spins. Since the AUX Fan is right in front of the condenser, I think this might have something to do with the AC problem.

What are things to check about why the fan is no longer running?

The fan is actuated when the a/c refrigerant reaches a specified temperature. It the a/c system is not working, that will never occur. So the inop fan is most likely a symptom of some other a/c problem, not the cause of the a/c failure.

If the a/c failed on the first day that you owned the vehicle, I would suspect that the system has a leak (known to the seller) and was charged up so that it would work long enough to make the sale.