Thanks for all the helpful responses. We have checked the screens and they are not plugged. Another thing that leads us to believe that it's a valve is that when you set the machine on hot cycle, it fills faster than when you set it on warm. We haven't tried reversing the connections because...
The cold water hose is fine (checked it), but the machine will not accept cold water at all. Hot water cycle runs all the way through; warm water cycle gets stuck on rinse cycle; cold water cycle will not work at all. Took plate off back. There is a blue box where the hot and cold water...