@kingofspades the very first thing you want to do is to replace your battery. Since ifixit does not yet have a guide for that, use something like this video Batteries are readily available at plenty of online stores. Just make sure you get the one for your version.
If a new battery does not accomplish this, replace the charging flex as well. Use something like this video for that. The flex is readily available at places like this (example ony) and many others.
While you work on your phone, take lots of pictures. Once you are done with it, take those pictures and create a guide for iFixit. That will help the next person that has the same problem as you do. It's easy and fun to create these guides. https://ifixit.com/Guide/new The iFixit community will appreciate this.