To force restart an SE you don’t use the Home and power buttons, as the Home button is not a physical button, it is touch sensitive and thus cannot trigger the restart firmware. Instead:
- Press and quickly release VOLUME UP
- Press and quickly release VOLUME DOWN
- Hold the POWER button until an Apple logo appears (15-30 seconds), ignoring "slide to power off"
The operative word here is QUICKLY; and try it a couple of times, the timing is a little tricky.
The phone may still be broken, but try the above first.