Answer to: Cell phone, wont chargeIt sounds like the jack where the charger plugs in is either loose or has a short. I would take the phone in and have them check it. It has to be the battery or charger or phone jack and based on what you stated the problem looks like a loose connection.
Answer to: What adhesive / glue is best for screen replacement?I like Loctite brand super glue which can be purchased at hardware stores and other locations where superglue is sold. Hope this helps.