iPhone 7 screen is frozen on the shutdown screen
For iPhone 7 and 8, you need to hold down Lock and Volume Down at the same time to reboot. Older iPhones use Lock and Home button.

If you cannot restart the phone this way, you may have to use DFU mode.

(Note: These links are hosted by Verizon, but will work with any iPhone 7 or 8 on any carrier.)