Thank you! You saved me! For some reason the only key I did not try is an UP key, and it was not clear for me from the UI hints that I have to press it to enter the door.
Now when I played it, that a very, very clever game actually! Beautifully design and well executed! Starting a level over and over after one mistake is not my thing, but even with that I finished half levels because of how interesting they are.
Great game!