。
She was dying to leave the party.
Literal
She [topic-は] party [object-を] want-to-leave [unbearably-てしょうがなかった].
~たくてしょうがない is one of two near-synonymous emphatic-desire constructions (with ~たくてたまらない), both meaning 'so badly want to X that one can't stand it.' しょうがない ('there's nothing to be done about it') captures the helplessness of an overwhelming impulse. The plain past しょうがなかった here puts the desperation in a recalled past moment — perhaps the party had dragged on too long, or she had something pressing elsewhere. Note でたい (出たい, 'want to leave/exit'), with 出る taking を for the place exited from.