Check the trunk from top to bottom for rotting areas, with or without oozing white or orange stuff. If none, leave it alone if you can bear to, and just wait - it may yet shoot new growth up the trunk or from the base, and when it does, you can saw the trunk down to that point. You may have to wait till June for anything to appear though. If you have oozing orange areas, or obvious rotting, cut down beyond that point now and see if anything grows later on.