As Madison said, the key is in Penelope's bedroom at Seagram. Now we just have to find out where that is.
After Penelope tells you to get the peridot, go to the lobby at Seagram to see that the desk nurse is now looking at a yellow chart.
As Joey, look at the chart to find that Penelope's room is 12G. Take the elevator to the 12th floor.
In her room, Joey can see that the key is hanging off the chair. Blow on it --
-- to find that it only falls a short way, and he can't blow it any further because of the carpet. Blast!
Let's reset the puzzle. Go back down to the lobby and tell the nurse that Penelope's room needs to be cleaned; go back up to find the key back on the chair. Now how do we solve this situation?
What we need here is a variation on the old newspaper-under-the-door gimmick, where you push a newspaper under the door, push the key out of the lock onto the newspaper, and pull them both under the door.
You need a small stiff slick piece of paper or cardstock that you can push under the door and get Joey to blow it over to the chair, so that when he blows the key down it falls on the card. You also need a piece of string or something to tie onto that card so you can then pull card and key back under the door.
There's a ball of yarn in front of Penelope that she doesn't want. For the card, take a brochure from the lobby. And how handy -- if you look at it, you'll see it already has a hole in it. (Yes, the bright red hole punch on the desk is just a red herring to make you mad because you can't use it.)
Drag the yarn onto the card to combine them. Now you're ready to get that key.
The procedure is: Rosa pushes the brochure with yarn tied on it under the door. Joey blows on it twice to get it just under the chair, then blows on the key. Rosa takes the brochure, and the key with it.