Liquid keyboard damage on MB Air - password keys don’t work even with USB keyboard
Physical damage simply cannot “fry” software; it’s impossible.  The most likely cause is that something is shorted in the MacBook keyboard and it’s conflicting with the same signals being sent by the USB keyboard.

Disconnect the keyboard from the logic board and then use use the USB keyboard to login.  While it will get you up and running, it’s not a permanent fix.  The top case will have to be replaced.

See Keyboard key stuck or not being recognized; how to fix for more details