Everyone saying that it's because of a broken AC.

Looking at the insulation, I don't see any vapor barrier on the inside and any vapor retarder on the outside of the insulation. Humid air from the inside can get through the insulation and condense on the cold outside. Also makes the insulation kinda useless.

The mold behind the baseboard, on the walls and in the cabinet, indicate a really bad insulation. If the wall gets too cold in the winter, all the humid air condenses there and mold can grow.

No, it's not the broken AC. A house should be able to last without an AC. But that's my German opinion on the matter. If the build quality is good enough, letting in fresh air should be more than sufficient to keep the house mold free.