Did it ask you for the key, or did it ask you to activate? Usually, it asks you if you need to activate, and if you say yes, it takes you to the Battle.net account website to enter a key.
This doesn't mean you need to do this!
Go into your Battle.net account here: http://us.battle.net/account
Under "Your Game Accounts", you should have Diablo III listed. Click on it.
If it says "ACTIVE" Under ACCOUNT STATUS, you are good to go, and you do not need a key or activation.
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