Oooh. It's been ages, and I could be completely off-base, but..

Isn't there a story about an arcade game? That transforms the player? Somehow the game goes farther than it's supposed to, because Danny/Dani had the power. The wizard had to make things right, and takes the transformed Dani on as an apprentice.

That sticks in my mind as the appearance of Dani.

Or, I'm completely wrong.