Check the trunk from top to bottom - you're looking for soft, soggy areas, or blackened areas. You'll probably find its soggy or soft at the top because it sounds like the growing tips have died, but wherever you find these areas, you need to cut the plant down beyond that point - and if that's near the base, that's where you cut it. It should send out new growth at least from the roots or near the base, and often up any remaining, healthy stem after cutting.