When an iPhone battery is completely drained it may take 30 minutes or more before the iPhone responds. After 30 minutes on the charger reset the iPhone. Press and hold both the Home button and the Sleep/Wake button continuously until the Apple logo appears. Then release the button and let the device restart. You will not lose data doing this. It's like a computer reboot.
If the phone restarts let it continue charge until the battery is 100%. If the phone does not restart make an appointment at an Apple Store to have your device examined by a technician. Or contact Apple Support. Be sure to back up your device before taking or sending it to Apple.