Chosen Solution
I got a Iphone 5 of ebay, knowing it didnt work. The screen was shattered, and I tested the battery and it was dead. I replaced both the battery and the screen. It still will not turn on, and will not be recognized by itunes. The phone does get warm while charging.
Could be a defective screen, or a bad battery or even the charging port. Do you ever hear the phone boot up?
