There are several things you can do to get your iPhone turned back on if it isn’t turning on as usual. The first thing to do is try to recharge it just to make sure it has enough power to turn on. If your battery is too low, your iPhone won’t turn on as it stores whatever energy is available in order to preserve the settings and any saved data.
If it seems as if your iPhone is not charging properly, it could be because the charger or cable is bad. Try replacing those, and also make sure there is no lint or other blockages in the dock or cable that would keep the iPhone from charging. Also, try to charge the iPhone directly through the computer instead of a USB port.
If you know your iPhone is charged and it still isn’t turning on, press the Hold and Home buttons for twenty to thirty seconds to see if the Apple logo appears and the boot up process starts. If this doesn’t work, you may have to restore the iPhone to factory settings. This will erase all the data and settings, but if you have a backup you can sync that back into the iPhone later to restore what you’ve saved.
How to Restore When iPhone Isn’t On:
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Connect the iPhone the dock connector, not a computer yet.
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Press the Home button.
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Now plug the cable into the computer.
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iTunes will open and put iPhone into recovery mode.
If the iPhone still isn’t turning on, or booting up all the way, try to get it started in DFU mode. If this still doesn’t help, make sure you aren’t having a proximity sensor problem. Sometimes issues with the proximity sensor will cause the screen to shut off when it shouldn’t. To correct this issue, hold down Home and Hold to restart the iPhone. When it restarts, choose Settings>General>Reset, then choose Reset All Settings and confirm reset.
Resource: About iPod