The riot was out of control.

Literal

Riot [topic-は] hand [subject-が] can't-be-attached state was.

手が付けられない is the idiom for 'uncontrollable' — literally 'hands can't be put to it,' picturing a situation no one can lay a hand on. The potential 付けられない conveys inability. 状態だった wraps the idiom in a noun predicate: 'was in a state of [uncontrollable].' Both 付ける and つける spellings are standard; the kanji form feels slightly more deliberate.