Hello Friend.
When the phone don´t turn on, try these options.
Replace the battery, this can solve the problem, the malfunction of the battery, can influence that the phone does not start.
Try to turn on the phone without the battery is connected. Disconnect the battery, and connect iPhone into the charger and turn on iPhone. If he turn on usually is the battery problem.
If not turn on, connects new un dock connector, and turn on the iPhone, if turn on, the problem is the dock connector.
This problem is kind of boring.
Good job!