Not exactly sure how to do that, is it the same as enabling legacy support?
Some BIOS have a setting to use USB keyboards and mice in legacy mode. This could enable it to work even if Windows setup does not load the proper USB driver. If this is what you were referring to, go for it.
I reject avromie7's answer of using a USB keyboard. I assume he assumed that you had been using a PS/2 keyboard until now and that a USB keyboard would be better. If you have been using a USB keyboard and are able to try a PS/2 keyboard instead, this could help, as it doesn't require drivers. This can only help if your system board actually has a PS/2 port (purple for keyboard, green for mouse); going through an adapter to the computer's USB port is no better than a USB keyboard.
This is a known issue with some builds of Windows on certain computers. If the above two changes are not possible for you system board, perhaps getting another build of Windows could help.
I am actually working the identical problem on another HP model now, trying to install Windows 10.