I believe you are having this problem because the transceiver unit connects to a USB port on your computer but you have not set the BIOS to handle USB keyboards. Without the proper BIOS setting, your keyboard is only usable once an operating system that is capable of recognizing USB input devices has been loaded. Furthermore, you will be having difficulty when you attempt to reinstall Windows, since Windows installer is not able to recognize USB input devices all by itself -- it needs assistance from the BIOS.
What you have to do now is grab a working PS/2 keyboard and plug it in to your computer so that you can enter the BIOS settings menu and locate then alter the relevant setting/settings in order to be able to use your USB input device outside of an operating system environment. You would have refer to the users manual that came with your motherboard to know which setting/settings to change but, as far as I know, it is typically dubbed 'USB Legacy Support' or 'USB Keyboard Support'.