Why won't my iPhone turn on?

Hi.

First of all try to connect it to a power source and wait just a few of minutes, maybe it's only a battery problem.

Otherwise, you can try to put the iPhone in the DFU mode and connect it to the Mac/Pc.

Keep me update.

Bye.

First thing to try is to reset your device. Press and hold the Home and Sleep buttons simultaneously ignoring the red slider should one appear until the Apple logo appears. Let go of the buttons and let the device restart. See if that fixes your problem.

This is a possible solution, but not a first choice. First choice is a simple reset, and described by Ralph.