So I played through the game normally, and got to Twinkle Park, then the ID keycard appeared where it should have. Opened the big metal door with it, but placed it on the floor before the two other doors, because I thought that I didn't need it for them.

Then I came back, and the keycard was gone. And it refused to respawn, even when I reset the game.

Is there a way around this? Because, I am certainly not playing through the game again. I don't even care if I have to use cheats, is there a way to get through the doors?