When putting it back together, I replugged in all three of the ribbon cables and powered on the phone to test before putting everything back together. All was OK except for the Home button, it had no effect when pressed. I ended up unplugging and replugging the 3 ribbon cables a few times and retrying. I then cleaned the connectors using a can of compressed air, screwed the little silver cover back on and snapped the whole phone back together, hoping everything would be fine. It was. I don't know if the problem was a dirty connector, or if you need to close the phone to make the home button work again.
I recommend wiping the plastic prying tool after lifting the screen off, it gets dirty from the gunk build up and some of that could eventually fall inside the phone.
My battery was really stuck, so much that the plastic tab broke when pulling. I followed someones advice to heat the back of the phone with a hair dryer, still wasn't super easy but I managed to get the battery out, only deforming it slightly.