Running standard HID complaint keyboard and driver.
So thats a us keyboard layout with english (
US) system-lang and a Microsoft driver? I'm thinking not...
The restart works because windows just stores the settings during a reboot to save some time but when you shut down/ start up it goes to the motherboard and loads some drivers from there or from a special back up part of the hdd (
in the case of most laptops)... I would assume one of those drivers is a keyboard driver (
perhaps outdated or for different keyboard settings) but close enough that Microsoft lets it get past, hence the problem.
Option 1; get a new keyboard and test that one... I'd do this anyway just to say this keyboard isn't defective.
Option 2...