Is the shifter sloppy and loose? Did you check the shift linkage bushings? Try and push the shift handle all the way forward and to the upper left. May have to try it a number of times. Not sure if a check on the neutral safety switch would have caught this or not as your nss is fine and the linkage is in limbo because the bushings are probably severely worn or my guess there are totally gone as in non existent. Had this happen very recently. Thought it was a dead battery as well with the no start, not even a click.