post.user_wrote.label:
It's not completely clear whether the 3rd party provider opened the phone or not. I hope the OP schedules an appointment at the Apple Store Genius bar and asks as nicely as possible for an out of warranty replacement. That would be the best solution they can hope for. It will cost $299, but they'd be getting a fully refurbished phone and a 3 month guarantee to boot.
The last time I was at an Apple Store asking about the whole battery thing I mentioned aftermarket parts or repairs. I was told that it's really up to the supervisor to make the call. The way it was explained to me was that they don't want to be responsible for something they can't fix because someone else messed it up. Of course if it doesn't work at all then that's a different situation.
For the OP, did you at least try to plug it in to whatever machine you do your backups? I did that with an iPad Mini 2 that had its glass totally obliterated, the LCD severely cracked, and the home button fallen off from a really nasty impact. It still backs up just fine. The backlight glows white through the LCD cracks. It even shows up on Find My iPhone and responds to the remote alarm. However, if the display is gone, then it's probably going to need the full "repair" replacement cost.