Yeah, they've probably been saying that for years. Only practical option is the tourist police. And all they can do is ask/negotiate/translate for you with the hotel. They wouldn't be able to force them to refund anything, but sometimes just their presence is helps.
If you stay though, you wouldn't be able to get anything.
Hot water is generally made in room (instant hot water heater). I assume the unit in your room is broken? They can't switch you rooms? Who did you book with, direclty with hotel?
It's very possible they prioritize applications based on their intended departure date. Since you're not leaving for a month, your application might just be on the back of the list, regardless of when you applied.
That's what I understood from their response anyway.