The update is done within windows, you just launch the executable, as the instructions state.
That said, I highly doubt a bios update will fix that issue, and when you flash the bios, it will reset all your settings. What if you can't get into the setup then? Do you have a keyboard that does allow you to get into the bios? I would use that to go in and make sure all your USB settings are enabled. I would also make sure the new keyboard is not plugged into a USB3 port, or that USB3 legacy support is enabled.