Please confirm if any of the other ports on the back of the motherboard are working. Furthermore, test the system out of the chassis, placed on a non-conductive surface like a newspaper, a magazine or something similar, clear the CMOS removing the CMOS battery and all power cables from the power supply to the motherboard, leaving the system without power for 20 minutes at least, disconnect the USB front panel you have connected to the motherboard, after that place back the power connections from the power supply and try a BIOS update.
Check if there is any excalamtion marks on the Device Manager. Check if the USB ports work in the operating system running it under safe mode too.
And try again into the system BIOS.
Be sure to use only corded keyboard and mouse devices in order to troubleshoot this.
Thank you for the answer. I did as you suggested, unfortunately it didn't help.
All the ports on the back are fine, except for the PS/2 and the 2 USB ports next to it (all three of those ports ar in one block mounted on the motherboard). There are no exclamation marks on the Device Manager. The warning I get about missing keyboard appears before the OS loaded right after the BIOS screen with the Intel logo. I used corded keyboard.