English isn't my first language, but I think there are more pitfalls here than what's apparent at first sight.
I believe that if the meaning is "made me interested in ...", then the correct spelling is "piqued my interest."
But "peaked my interest" is grammatically correct ('peak' is a verb, after all), but with a different meaning: "reached the height of my possible interest in ...", so the phrase:
Disney is starting to peak my interest.
would actually mean/imply something like "Disney is starting to make me less interested", since after you've reached the peak, there's only one way you can go.
If you follow this thought sequence, and start looking at:
Disney is starting to peek my interest.
you end up spooked.