Try to restore the phone. It will probably do nothing, but it could fix the problem. The one thing you should do is let it do a backup first, to be sure the phone is backed up. If that doesn't help replace the battery in the phone. You can find the guide here and the battery here.
Depending on the tools you have, there's a chance you could strip the Pentalobe screws on the phone. These screws are easy enough to strip, replacement may be needed. The screws can be found in the parts section of this guide. As of recent times, you may no longer need screws to deal with the damage. You can find Pentalobe drivers as standalone items, or in the driver bit kits. But if you lose or strip them you will need the replacement set.