If the lights goes on it only means the mouse/keyboard is getting power.
It doesn't mean there is any data transfer.
Try this:
Boot the system and wait e.g 15 minutes.
Disconnect the keyboard, wait 5 minutes.
Connect the keyboard to a other usb port.
The waiting times are just to make sure Windows can (or perhaps I would say should) notice something is changed and act accordingly.
The other usb port will tell (or at least should) tell Windows there is a "new" device attached and Window should install the drivers for it and configure them.
I can't promise this will work, but let's see what happens.