First (when charging) the iphone is off, only the charging circuit and display are working. Important is that the battery is not connected at this stage, except for charging. Now, when the apple logo appears, the iphone is connected to and powered by the battery. The battery has a connection, which gives the battery temperature. It is possible that if this is faulty and the iphone thinks it is to hot (battery) and won't turn the backlight on (which would heat up the battery even more). So, in short, try a new battery..
