The problem I'm having now is that the physical keyboard still no longer works. I then updated the BIOS and everything else with the newest ASUS T100 drivers and rebooted and was then able to select a different on-screen keyboard, so that was resolved.
I was unable to select a different on-screen keyboard after messing around with it for an hour or so. My physical keyboard stopped working after a accidently chose the on screen logical stylus/handwriting keyboard.