Turns out it's not the battery connector or the battery that's busted but instead the charger which we're both using, it's third party and the rubber around the connector has been tearing, I noticed that it makes a buzzing sound when I move the cable and if it's plugged in to the computer it makes it short out. I've ordered a new charger.
My headphone jack had stopped holding my headphones in place meaning that the headphones would pop out of the jack very easily. Replacing the jack using this guide was a breeze once the screen had been removed which was the most difficult part of the repair.
I did not have a suction cup to help lift the screen which I in retrospect would recommend anyone doing this repair to get.