Hi,
Try these steps, if none of these steps work please take your phone to your local Apple Store
Restart
Having checked power you should also try restarting the device. Press down on the Hold button (the single button at the top right or right hand side of your iPhone) for a few seconds. Does your iPhone start up?
It didn’t start up? Sorry about that. Let’s try a hard reset: Hold down the on/off button and Home button at the same time for 10-30-seconds. Don’t let go of them until the Apple logo appears (if it does). What should happen is that your iPhone will start itself up again, but if nothing has happened after holding the buttons for 30-seconds you’ll need to try something new.
Restore (if you have a backup of you iPhone)
You may need to restore your iPhone. You’ll need the latest version of iTunes installed on your Mac or Windows machine and you’ll need to connect your iPhone using its cable. Its icon should appear in iTunes, beside the ones that live just under the Play button. Click on it and then select Restore from the options available there. I do hope you’ve been backing up your iPhone, but if you have not and if the smartphone does startup you’ll be able to back it up now. Once you’ve done so you can continue with the Restore operation.
Recover Mode
If nothing’s worked, then you might want to put your iPhone into Recovery Mode. The bad news is that doing so erases everything – all the data – on your iPhone. Hopefully you have a recent backup in iCloud or on your computer. To enter Recovery Mode you must switch your iPhone off and connect it to your computer.
While it is connected you must force restart it. Press and hold both the Sleep/Wake and Home button for at least 10 seconds, don't release them when you see the Apple logo, keep holding the buttons down until you see the recovery mode screen. You should be asked if you want to Restore or Update your iPhone. Choose Update and iTunes will try to reinstall iOS without devouring all your data. Over to Apple who says: “Wait while iTunes downloads the software for your device.
If the download takes more than 15 minutes and your device exits recovery mode, you'll need to repeat these steps and choose Restore instead of Update when you get back to this step.” You’ll need to set your device up again once this is all over.