In Level 13 of World Escape, the door key is hidden inside a secret compartment in the Turkish lute. You have to play the combination tune in order to access the compartment. The music sheet is hidden somewhere in the room.
Below is a complete walkthrough. If you want to pass the level without going through the complete game play, jump to the Fast Short-Cut Cheat.
1. Tissue Paper: Open left cabinet door. Grab a piece of tissue paper.
2. Cup: Go over to the coffee table. Use the tissue paper to clean the coffee stain. Get password: 7414.
3. Password: Go back to the cabinet. Unlock the right cabinet door with combination: 7414. Retrieve a knife.
4. Painting: Check out the wall decoration. Get a drawer handle from the top of the decoration.
5. Drawer: Install drawer handle. Open bottom drawer. Get a wirecutter head.
6. Sofa: Look under pillow. Pick up a wirecutter handle. You now have a working wirecutter.
7. Window: Check out the window. Use the wirecutter to remove a piece of wire between the curtains.
8. Water dispenser: Use the knife to poke a hole in the water container. Insert wire. Retrieve a key.
9. Music sheet: Unlock top cabinet doors. Grab a notebook containing the music sheet.
10. Turkish Lute: Locate Turkish lute next to the sofa. Read the music from the notebook. Play in the order as shown in the image. A secret compartment will reveal. Get the door key.
Fast Short-Cut Cheat
Skip steps 1-9. Follow steps 10 and 11 to pass the level.