That would be "She was dying of hunger". Though I'd like to point out that in my previous comment I wasn't completely correct when I said that "moriva" is past tense. It's actually called past continuous I believe, and it actually usually is translated more along the lines of "She was dying of hunger" rather than "She died of hunger". But both can work.
Technically the true past tense would be "Lei morì di fame" but nobody actually uses this form much in speaking, though it can turn up in written material.
The fact that the past tense is so little-used (instead replaced by the present perfect or past continuous) is why Duolingo doesn't teach past tense until almost the very end of the tree.