I don't know this answer is useful for you or not. Anyway I send it to you.
I like to play. 私は遊ぶのが好きです。
※はa particle to express a theme/topic. がhere is a case particle to express an object to like, dislike, be good at, not to be good at・・・. This が is different from nominative case particle が for example 私は足が速い I run fast. Case particles(が, が, を, に, へ, より, から, で, と, の・・・) work as connecters to combine a subject, object to like・・・, object, place, direction, criteria, starting point, means, opponent/partner, possessive・・・. はis used to describe the state has already existed. 私が日本人であるコト→ 私は日本人である/だ/です。I an a Japanese. 地球が回っているコト→ 地球は回っている。The earth turns around. When がis used as a subject of the main subject of a sentence, it describes a new state. 雨が降ってきたコト→あっ、雨が降ってきた!Oh, it rained! /Oh, it has begun to rain!
I think playing in the yard is fun. 私は庭で遊ぶのはおもしろいと思います。
私が庭で遊ぶのが面白いと思うコト(a state has already existed)→ 私は庭で遊ぶのはおもしろいと思います。If you are asked "What do you think is interesting?", you should say "私は庭で遊ぶのがおもしろいと思います。I think 'playing in the yard' is. " This が is pronounced higher and louder to be emphasized. "~が" is a focused word(prominence).
I drive a blue car.
私は青い車を運転する/している。
私が青い車を運転する/しているコト(a state has already existed)→ 私は青い車を運転する/している。