I would try to put it in dfu mode and restore just hold in the top and bottom buttons for 10 seconds and let go of the top keep holding the bottom for 30 and plug into iTunes and try a restore
Is is possible the power or home buttons are broken? Did you have any button problems before this happened?
Try holding the home button then plug into computer. If the phone was powered off, iTunes should start and identify the ip4 in recovery mode and the ip4 will have the 'connect to iTunes' displayed. If that works, do nothing. Hold the power and home buttons for 10 secs, the phone will power off and exit recovery mode. No changes will be made.
Turn up the computer sound. While it's connected (and iTunes says 'recovery mode') .... hold both buttons for 10+ seconds (or until you hear a high-low beep. Do you hear the computer beep? If you hear a beep, the iPhone has turned off.
^If you don't get a sound when holding the home/power button for 10+ seconds and iTunes still shows the device in recovery mode ... then the device is not turning off. Not sure how to help. Need to start looking outside the box (hardware button, cables, reload iTunes, computer).
I might try to restore anyway. Up to you. It's not-normal you can't power off with both buttons.