If the log out button doesnt log you out, click here.
Scroll down to register to old CP.
All credit goes to ClubPenguinProject
How to Register to (old) Club Penguin
If you have a penguin for the new cp, you can't use it for the old one. To create an account you don't need an e-mail, all you have to do is click on Start and Create a New Penguin and Sign Up.