I have a 220 volt 22,000 btu through-the-wall a/c which has worked great for the past 15 years without a problem but yesterday I turned it on and it wasn’t working. it’s mounted in a metal sleeve screwed into the framing and the actual guts of the a/c seem to slide right out of the sleeve. When I turn it on there’s no no fan and and no cool air coming out. The compressor makes a loud humming noise for about 5 seconds then stops and then comes on again and stops. I’m suspecting the the compressor is shot. When i took the plastic front peice off I noiticed the fins of the front coil were filled with some black mold and now I’m suspecting the insides and back coil are probably filled with mold too. Because of that I’m thinking of just buying a new one the same size and try to put it in the existing sleeve. The electronics seem to work but I’m suprised there’s no fan. Are these things even possible to fix or just scrap it and get a new one? I think it’s possible it could be not getting enough airflow cause it’s clogged with mold or the compressor could of just died because because I’ve used it a lot every summer.
Sounds like a bad motor-start capacitor. If that’s all it is, it’s a $30 fix.
If there’s a chance it’s full of mold, though, I’d get a new one. You don’t want it blowing spores into your room.
15 years get a new one.
I agree with this but it does need service and a good cleaning.
are the capacitors usually what goes wrong with these things? That seems likely to me because it seems odd for the fan and compressor to both go dead at the same time. Unless there is some electronic circuitry which is not sending the proper signal at the proper time.
From the way it sounds it definitely needs a cleaning. Really dirty coils could cause the compressor to overwork and overheat and trip out on the internal overload. That wouldn’t cause the fan to shut down though. I suspect you might have a capacitor problem causing both to not work.
A new wall a/c (that’s what they’re called when in a sleeve like that) at that capacity is likely over $500 so a fix might be worthwhile. Also it may not be black mold per se, it could just be wet dust and dirt accumulation. Regardless it needs a good cleaning, preferably outside with a hose, just be careful not to bend the metal fins. 
Note it’s going to be extremely heavy too, more than you may think, and the overwhelming majority of that weight is the compressor which is almost certainly not in the middle, so expect it to be very unbalanced.