I beat the game with both Chris and Jill. I started a new game choosing normal this time. I had thought I would have the key already, but it's not in my inventory. The closet door is there, but where ...

If you complete the game on Normal or Hard mode, you'll find the Closet Key in Rebecca's Inventory when you start a new game. Billy will get a suit and Rebecca will get a leather outfit or a cowgirl ...