You don't need a key, the game is already attached to your Battle.net account.
Support Information Administrator
Go to: http://us.battle.net/account
Under "My Game Accounts" you should have Diablo 3. Click on it.
Under "ACCOUNT STATUS", it should say "ACTIVE". If so, you are good to go, and already activated.
The installer simply asks you to activate if you haven't already. So you can tell it you are activated, and it will proceed normally.
Threats of violence. We take these seriously and will alert the proper authorities.
Posts containing personal information about other players. This includes physical addresses, e-mail addresses, phone numbers, and inappropriate photos and/or videos.
Harassing or discriminatory language. This will not be tolerated.