When you signed up the 1st time, you should have gotten a screen with the key - which you should have copied, printed or at least wrote the key down.
At the same time, you should have gotten a copy of the key, along with all your instructions in your Hotmail inbox. The key should have been at the VERY bottom of that email.
Now then, if you deleted the email, you can go through the sign up procedure and get another key. No hassle - except for having to fill out the forms again.