Seriously, answering that question should probably be their number 1 priority. Right now they can't say that "What Yahoo! does is X," much less "Yahoo! is #1 at X," for any X. They need a direction. Answering that question won't solve all of their problems, not by a hell of a long shot, but anything that is effective at solving their problems will necessitate answering that question.
They've decided they're not a search engine. They still sort of seem to think they're a portal; I don't see a lot of people really caring about portals anymore, but maybe if they push hard they could bring that concept back. If they really wanted to be bold, they could try to crack the perennially difficult nut of monetizing quality content on the internet. If they could manage that, they could become the go-to content publisher on the web.
From what I understand of their corporate culture, they probably need a leader that can make changes there as well. They don't need to become Google or a "start-up culture," but they need more focus on product quality instead of the treadmill.