Try a native PS/2 keyboard if your motherboard supports it. That's what I use (I even use it full-time in Windows so I don't have to switch when I want to check or change any BIOS settings).
Mouse not essential to navigate around BIOS configuration screens & make changes, all can be done with keyboard (with a functioning keyboard of course).
You can get a native PS/2 keyboard from Amazon, all those on the high street are USB nowadays.
Don't forget, PS/2 ports are not hot-pluggable like USB ports, so shut down PC before plugging PS/2 keyboard in.