I realize that this thread is quite old, but I may have found an answer. If the iPhone is turned on '''before''' the LCD and digitizer are physically connected, then LCD and digitizer are not found by OS, and they never turn on, even if connected later.
Solution: disassemble the phone, disconnect the circuit board, then reassemble, taking caution '''not to press the power button before connecting LCD'''.
Possible solution: hold power and home button together to reset the phone.