Spongy Drywall near window and fireplace?

I went to hang a curtain rod in a house we just purchased. Previous owners had rods in the same area. When I went to drill in the molly's the 8in by 8in section of the wall seems very soft and the paint is peeling and crumbling off very easily. The Molly's won't stay in when I try to drill in the screws with the hook, they fall right out because the wall is too soft. What can we do???? What is wrong with our wall?