I've been having the same problem for like 30 minutes now and finally found this on the Blizzard support website:
"If you purchased or pre-ordered Diablo III through our online store or are part of the WoW Annual Pass promotion, you will not have to enter an Authentication Key to activate the game license for your account, this was done automatically during the purchase process. Once you have installed the game, simply log in with your Battle.net credentials."
We should be good to go? I'm installing now and will let you know!