Q: reboot

Press the Sleep/Wake and Home buttons and hold them for at least 10 seconds.

If this does not help, take a look these Apple Support articles:

If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on - Apple Support

Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.

As a final step, try the recovery mode. Turn your device off, then plug it to your computer with the home button pressed. Keep the Home button pressed until you see the iTunes logo on the screen of your iPhone. After that on your computer you should see the iTunes window saying your iPhone needs to be restored to factory settings. Click on the restore button.

More info here: https://support.apple.com/en-us/HT201263

Make an appointment at the Apple Genius Bar for service. If needed find an Apple Store - Find a Store - Apple.

Have you tried any troubleshooting?

1. Restart:  Press On/Off button until the Slide to Power Off slider appears, select Slide to Power Off and, after It shuts down, press the On/Off button until the Apple  logo appears.
2. Reset:  Press the Home and On/Off buttons at the same time and hold them until the Apple logo appears (about 10-15 seconds).
3. Restore:  Connect your iPhone to iTunes on your computer, backup, and then select Restore to Factory