Actually on most MoBo's made mid decade or later USB drivers are NOT part of
the OS but in MoBo BIOS and are recognized natively.
They MUST be "natively recognized"
Sometime around 2005-2006 computer manufactures started making computers that were intended to be run with USB mouse and keyboard natively and you have to go into setup and selective "legacy devices" to on to get a PS2 mouse or keyboard recognized at all, this of course presumes that
the MoBo even has PS2 jacks....
Because many MoBo's made 2006 or later didn't bother including PS2 jacks for legacy keyboard and mouse...
If the USB drivers were part of the OS there'd be no way to POST the computer
let alone install an OS unless the USB was in BIOS/CMOS...
Frankly I'd check to see what the setings were in setup and if you are using
USB keyboard and mouse turn "legacy devices" (PS2 keyboard and mouse) to OFF
The "new hardware detected" and "installing drivers" when you connect a USB keyboard
do not generally relate to the keyboard functions, but to the often included USB hub or
Multimedia functions that are included in/on many keyboards.
Why should you need a driver for a keyboard if the computer will typically fail to POST
when it fails to detect a keyboard when booting?
BTW, this set of symptoms can also be caused by a dead dying CMOS battery,
which would cause your computer to lose it's settings on an a power off reboot
Spend $3 on a new CR2032 (they also come in two packs for ~$4) before investigating the problem further. this comes under the heading of"always check stupid stuff first!"