Digital download customers are now restricted to the starter edition section of the game: part of Act 1, a level cap of 13, no auction house access, and limited interaction with other players. These restrictions do not apply to those who purchased the retail box of the game.
A Blizzard employee explained the unlock delay in a forum post: "Outside of the issue that we fixed, digital purchases do require a review period before they kick over from Starter to Full editions. We apologize for the inconvenience, but it is a necessary step to combat fraud and other malicious activities that can weaken everyone's play experience. The delay is no longer than three days, and is often much quicker than that. Hang tight."
This follows this morning's news that the South Korean government is twisting Blizzard's arm to make the studio issue refunds for dissatisfied customers.
[Thanks to Marc for the tip!]