LOL -- sorry but have to laugh at the Logitech sites suggestion for fixing it (Logitech Connection Utility!!)
This standalone version of the Logitech Connection Utility program is for use on Windows systems and is not available for Mac. It can be used to reconnect supported keyboards or mice with a replacement receiver or when the connection is lost.
To reconnect your keyboard or mouse to its receiver:
Launch the Connection Utility:
Without SetPoint installed (Windows only):
Download, save and run the Connection Utility.
With SetPoint 4.8 or below installed (Windows only):
Click Start > Run > type "C:\Program Files\Logitech\SetPoint\Connect.exe" and press Enter.
With SetPoint 6.0 or 6.15:
Click Start > Run > type "C:\Program Files\Logitech\SetPointP\Connect.exe" and press Enter.
With SetPoint 6.20 or above:
Click Start > Run > type "C:\Program Files\Logitech\SetPointP\ConnectUtility.exe" and press Enter.
Follow the onscreen instructions to reconnect your keyboard or mouse.
-- they have you download a utility and type in some things from within window -- How exactly do you do that if the keyboard and mouse are not working !!
@OP -- do you have another keyboard you could use temporarily (PS2 or other wireless) -- If yes try using it instead and then Once inside windows plug in the USB receiver for the new keyboard and see if windows recognizes it as being connected. (it should auto install the driver needed) If it still doesn't work try using the lgitech utility above and see if it fixes it.
Also what MOBO do you have ? look in the BIOS for any settings for the USB ports and ensure that Legacy support is enabled for example on this Gigabyte MOBO there is this option that is diabled by default but should be enabled for windows using a USB port keyboard !
Port 60/64 Emulation
Enables or disables emulation of I/O ports 64h and 60h. This should be enabled for full legacy support for USB keyboards/mice in MS-DOS or in operating system that does not natively support USB devices. (Default: Disabled)