I have also the same problem.
When I upgraded my win 10 home to pro it happened after changing language. Possword field is not visible even when I restarted my pc.
It's been two day since I am not able to login my pc.
The problem for me happened only after closing the lid, which put the laptop into sleep mode - when 'woken' there was ususally no login box, so I had to switch-off using the power on/off switch, then reboot. The login box always appeared ok after switching the laptop off and rebooting.
Your problem appears much worse ... I would suggest you switch-off, then disconnect/remove the power lead and remove the battery ... leave unpowered for a few minutes to be sure, then reboot. Reinstalling Windows 10 would be another drastic suggestion.
I will try the last posted solution from Meglp (March 24th), but after I disabled the Win10 feature that puts the laptop to sleep when the lid is closed, I have not seen the problem so a little hesitant to re-enable that feature!