My old Rezound did this to me a few times.
Best way I saw it explained is that it went into some kind of mode where it would be in fastboot with the screen off.
So it won't charge and it won't boot...
My Rezound had an associated flash of the charge indicator when it was doing this - not the same flash that it does when it's completely dead.
I haven't seen any of my other HTC phones get into this mode.. unless the One does it too?