The dream of this day had begun to take shape when I was twelve, growing up in California. I had auditioned for the starring role in the 1959 movie The Diary of Anne Frank. I didn't get the part, but I found a whole new world in Anne Frank's diary.
I am rephrasing the highlighted parts above paragraph according to my knowledge. Please check I am right or wrong.
There is a vacancy in the movie (The Diary of Anne Frank) for a starring role. So they kept audition to select the best men/women for that starring role.
So the highlighted parts mean (I had participated in the audition where people were being selected for a starring role but I was rejected so I didn't get chance to part in that movie but I had read a whole story in the Anne Frank's diary.)
Please help me.
but I had read a whole story in the Anne Frank's diary
I agree with your interpretation, but I would change the above line to something like "but I read Anne's diary and it changed my perspective" or "it changed my view of the world."