Keyboard not working during startup and Win10 is in Legacy mode so UEFI option in troubleshoot menu is not there.
Option 1, disconnect system disk, enter bios, there is options to disable devices before booting, something like that, configure that so you can use your keyboard, reconnect the disk. Option 2, connect ps/2 keyboard Option 3, reformat on Uefi mode
#1 UEFI mode and legacy BOOT menu are two whole different things (mostly) unrelated each other. #2 if you are masochist and want to go to the GPT partitioning scheme, there isn't any need to reformat (almost always there isn't any need to reformat, unlless you're selling your PC or your HDD), any recent W10 comes with the mbr2gpt command. #3 is not clear from the 1st post if the OP's keyboard is physically broken or it's just the bios that's somewhat stuck. In the first case just use an external keyboard (USB is more than enough for any PC built in the last 15 years), in the second case just reset the bios disconnecting/shorting the backup battery.
If you have something like Fast Startup/Boot enabled in your bios then USB keyboard won't work until you get to windows. The mainboard manufacturer would have a tool/utility you can download that would allow you toggle this feature ON/OFF. ie, MSI have "MSI Fast Boot" in their bios/uefi and provide a "Fast Boot Utility"...
That's true as well, but usually FB works only if the previous shutdown was clean, easy to test, just shut down the PC (abruptly) with the long press of the power button, and the BIOS should take it in account not doing the fastboot in the next boot.