My iPhone 5s was badly water damaged this week. It won't "turn on" unless it's plugged in, but even when that happens the apple logo flashes and nothing happens afterwards. When I would plug it into my computer to try and back it up, iTunes would start but then it would say "waiting for phone" which was a problem cause I couldn t do anything. So I replaced the battery on it (so it could have a charge since my phone doesn't seem like it's charging anymore) to see if that would help but now when I plug it into iTunes it starts to update to iOS9 in order to back it up. The only improvement with the new battery is that when I start to back it up the iPhone updating screen shows up, but then iTunes says error 27 and gives up.
I haven't backed it up in months and have a bunch of stuff on it. Any help or ideas would be great. Thank you (also IIm trying to stay away from the website that you have to pay $60 to recover data from your phone)