If you are still stuck try restarting by going to the main menu.
Then play until the point you got stuck in.
Instead of using the crate you used last time to solve the puzzle you can use the other crate. Using the left one for me the righthand side crate pushed on top of the plate opened the door. The left one did not.
If that does not work then try setting your video settings to windowed and try it again starting from the menu.
I did both those things and it worked so either one of them could be the culprit for the unintended behavior.
Hope it helps