Thanks iFixit, battery replaced. Aside from the adhesive strips (they broke initially, but thanks to the heat of the initial battery drain, I’ve managed to pull them out in one step), the hardest part for me was reconnecting the screen cable connectors. I didn’t want to press too much because of the various advices, but doing that, there was some problem the first time I turn on the phone: white lines on the bottom of the screen, and the touch was not working from the middle center to the left. So, I’ve reopened the phone, disconnect all the cables, and reconnect them again, this time with a little bit more pression on the side (but not excessively).
