iPhone 7 has gone black, is in recovery mode and will not restart/restore.

Hi, any help much appreciated. Our son's iPhone 7 is about six months old, and it stopped working a couple of days ago. He was in the middle of watching something when it froze and then just went to black. Since then I've tried to reboot it using the side button + volume down buttons solution, but nothing, still dead. I then connected it to iTunes on my mac to try and restore it and eventually got the message that iTunes had detected a phone in 'recovery mode' and that I needed to restore the phone before I could use it. Fine, so I tried that but then, finally, I got the error message "The iPhone (NAME) could not be restored. An unknown error occurred (4014)." My iTunes is up to date so have I gone as far as I can. to try and fix this? The official apple advice page https://support.apple.com/en-us/HT201444 says that for error codes including this one which still persist, then I need to contact them. So I just thought I'd put this out there to you guys and see if there's anything left to try myself? Thanks very much.