Is it possible that the Task Sheet view has been corrupted? Try editing the Task Sheet view. Do you see any rows (view columns) that look goofy or have error messages in them? If so, try removing those error rows from the view and see if the problem disappears.
It’s a long shot, but I’ve seen weird things happen in views in 2013. For example, in our environment, you could cut tasks, but you can’t paste them. It turned out that the view had been corrupted and once it was “adjusted”, everything worked again as expected. Like I said, it’s a shot in the dark! 🙂