I've meesed with outboards a while this is the first I've seen where both prop and water pump don't work. I assume it is drive shaft related. Just quit working will motoring no other symptoms. Motor still idles fine.
What is your model? If you drop the LU, is the driveshaft in one piece?
NS25C3 2001 I'm not sure, I did notice there didn't seem to be any splines or a key just a smooth shaft.....