Hey blockboy21814, you should download iFunBox (Google it, it'll be the first link) and watch this video on how to back it up as well.
-Since you said that it turns on to the lockscreen when you plug it in the charger you should be able to back it up fine with iFunBox. However, if it's stuck on an apple loop while it's charging and you can't boot it up to the point where you see the lockscreen then you have no other option but to put your device under recovery mode and restore.
-After you back up, I'd recommend that you follow what PhoneOpsPlus said at his post at the bottom. That is only if it does the same thing after restoring.
-Let me know how it goes.
-Please accept this as the answer if it answered the question.