The units are supposed to stay upright so the compressor oil does not migrate. Once it's returned to upright and sits for an hour or so, the oil will return to the compressor. A certain amount of oil migrates throughout the unit during operation anyway, so that's not a concern. Since the AC was operating before, it's unlikely that turning it upside down caused any type of mechanical damage. The compressor is starting and trying to run, but what you are describing sounds like it's lost it's run capacitor. It's also very unlikely that being turned over would have damaged the cap in any way, so I would look for a wire that had come off of a terminal somewhere. And no, it doesn't need a hard start kit.
