Dingbatt: It sounds kind of terminal. Very occasionally my M7 just won't start up. Even though it has a full charge it acts as though it is dead flat. I put it on its original HTC charger for about 5 minutes and then do a hard reboot by holding the power button down for about 30 seconds (until capacitive buttons have lit up, gone dark again and then after a pause the phone buzzes and starts up).
You indicated a reboot to recovery attempt with the volume buttons, but I too had no luck when I tried that.
Yeah should be under warranty still as its under 2 years old.