Windows Key+P gives the monitor options. I wonder if it is stuck (or spilt/splashed liquid on keyboard).
Give it a good mashing.
I don't know why that would cause on-screen and external keyboards to play up though. Have you disconnected the original keyboard while trying the others?
Try tapping F8 at boot and see if you can get into Safe Mode Admin account.
Test keyboards again. Change password to blank for the moment if you can, on normal account.
Ps/2 keyboards require a reboot every time you reconnect. USB don't.