You did not say whether the house is frame or brick. Let's assume frame. The question is what does the ceiling (and actually the joists) do over by the wall? If the ceiling is down where the ceiling meets the wall then you may also have a problem in that wall. In that case you need to rip down the ceiling and the plaster on that wall and repair the wall along with the joists. In other words if the first 6" of joist by the wall are ok but it gets rotten after that then the wall is ok. If not and the joist is rotten all the way to the wall the wall is most likely involved.