Chosen Solution
Wow thats a long post, sounds like you have multiple problems. firstly the history of the phone is unknown so I would go for long screw damage on the lcd metal plate anchors for the blue screen. If a long screw is put into the wrong place this basically drills intot he circuit board and cuts tracks. This is a very expert fix if at all possible. This needs sorting 1st. long screw damage will cause blue screen of death, it can be intermittant. remove the lcd connector screws and have a look inside the thread hole and see what you can see, if you see anything that looks like copper your in trouble. also leave the screws out and see how the phone works as the long screw may still be used and causing problems. Other issues cauld be pry damage when you have removed the battery or just a crap battery but without fixing or ruling out the long screw damage your wasting your time.
