。
She was dying to go to the party.
Literal
She [topic-は] party [to-に] want-to-go [unbearably-てたまらなかった].
~たくてたまらない is the close cousin of ~たくてしょうがない, both meaning 'wanting to X so badly one can't bear it.' たまらない ('unbearable') comes from 堪らない (the negative of 堪る, 'to endure'), so the literal sense is 'one can't endure (the wanting).' The two are largely interchangeable; たまらない leans slightly more visceral and bodily, しょうがない slightly more resigned. The plain past ~なかった situates the unbearable wanting in a remembered past moment.