Happy Birthday!!
Location: Main House, in the attic accessible from Lucas' old room, in the cabinet at the top of the ladder.
Guide: You may want to play it through once on your own- it's an escape-the-room type puzzle, and it's not bad (though it is horrific). Once you've figured it all out, replay the tape with an eye for speed to get the 'Out Before Dessert' achievement, which involves solving the puzzle in under five minutes.
The steps there are-
Grab the candle from the automaton.
Hard left into the kitchen, then right into the cake room.
Stand in front of the cake to trigger Lucas's monologue, during which you should stand right in front of the keg.
The moment he's done talking, take the winding key.
Turn left and enter the box combo – doll in a noose, crow on a rock, baby (you discover this by using a telescope in the toilet, washed clean by the cake-room shower, on tv array past the kitchen, but we don't have that kind of time now). Grab the straw doll.
Walk to the stove and light the doll on fire, getting a dummy finger.
Light the candle.
Turn left and walk to the door past the tv screens. Ignite the cord to open the door
Near the far end of the room toward the right is a small yellow balloon mixed in with all the other balloons. You don't need be able to see it to get it, just be close enough to the object marker.
Go back toward the kitchen, but veering right before you reach to stove area. Attach the balloon to the gaspipe here. You'll wind up with a quill pen.
Return to the automaton. Use the dummy finger on its hand, then use the quill on its hand, then use the Windup Key on its torso.
Take you new code back to the balloon room, and enter it in the combo lock at the far end of the room, to the left.
Grab the valve wheel, and take it back to the cake room, using it on the pipe just inside the door, to the left.
Light the candle on the stove, and place it on the cake.
This doesn't end well for Clancy, alas, but you get an achievement out of it, and Ethan gains a bit of insight into a future challenge.