パーク/公園 is the OBJECT of 楽しかった in the first example sentence. The object is topicalized and the subject "I" is omitted. Thus, 公園は楽しかった actually means "I enjoyed a/the park". Similarly, the second example sentence 私も(公園が)とても楽しかった is "I, too, enjoyed it(= the park) very much".
が indicates the object of adjectives that express emotions/sense such like 怖い, 好きだ, 嫌いだ, 苦手だ, 痛い, state verbs such like わかる, 要る, できる, or potential forms/-tai forms of verbs.
e.g.
幽霊が怖い
I fear ghosts.
料理が苦手だ
I'm not good at cooking.
英語がわかる
I can understand English.
旅行するのにお金が要る
I need money to go to a trip.
英語が話せる
I can speak English.
寿司が食べたい
I want to eat sushi.