If one empty slot in not empty and you can no longer equip something to it than the only fix I found because I had the same problem is to prestige one level, carefull when you hack items and perks, if one slot is broken in the process than do not save and be sure to uncheck the cloud sync and than after quit the game download the saves from stean cloud again. You can use the cloud safe to keep "emergency" saves but if you are scared to use steam cloud just backup yourself the saves manually.