Had to read the "guide" to figure it out. I think the problem is that the puzzle doesn't really make sense (why does the key break upon entering the room - does it mean that keys break when players step into the room?) and the presentation doesn't help (as you appear to be stuck in a loop, giving the impression that the game has glitched out). The effect was pretty neat and meta though. Very atmospheric music, but the window is too small (which I guess is to help with that effect).
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Yes, the key breaks each time the player use it to open a door. So the only way to keep the key intact is to use the door already opened ... The main "puzzle" has got really sense, in contrary, and the concept of Meta Game has got more impact when the player thinks he'splaying a "normal" game that encounters a weird lopping situation (the "meta" concept is not artificial or arbitrary here, but the only way to solve the problem). Obviously a lot of player will not find THE solution (players can read the solution I've written, as you've done : it's for me a complete part of the game, a kind of real "out of the box"), but some have found how to do by themselves too.