If it's under warranty, I would assume that you do have recourse, but you'll have to send it away for most likely quite a while. That said, I have seen different websites online stating that Microsoft charges upwards of $100 to fix it (I don't know if this is the case if it's still under warranty).
If it's not under warranty, or if you'd like to do it on your own so you don't have to wait, there are numerous websites (possibly YouTube videos also) that have detailed step by step guides to fix the problem. Keep in mind that if the unit is still under warranty, attempting to fix it on your own will void it.
