I think a more literal translation would be: "It begins to interest her." That is, "to" is nominative and "ji" is accusative.
It is, exactly literal. Please click "REPORT - My answer should be accepted" under the sentence. Thank you.
"It is starting to interest her" is perfectly fine in English. However, "She is starting to have interest in it" is accepted.
This is where Czech word order can feel really strange. The subject in the third position.