Let me just go ahead and predict that Apple will inform you that it will cost more to repair the device than the device is worth, and then tell you your only option is to buy a new device, which is what they want you to do anyway. The more new devices they sell goes toward the next "Apple sold XXX new devices in the month of April" news headline.
If you have any repair facilities in your area, regardless of if they are "authorized" or not, get all the estimates you can and then you have to make the decision (1) if you want to get it fixed and (2) where to take it.
I will say that if you do a web search, you may come across a couple of places in the New York area that have a more than 100% success rate on repairing Apple devices.
Just my $0.02.