The washer needed a new lid switch. When the lid switch is broken, the washer acts as if the lid is open, so it fills with water, but does not advance to the next cycle. It is a very simple fix, even for someone like me, who has minimal experience fixing appliances. The lid switch is easy to get to, and only requires a Philips screwdriver and a 5/16 socket wrench. The video on this website shows exactly how to do it.