Usually you should replace those connectors every 5 years or whatever, or so they say. After recalling how a friend of his father had his hoses burst and flood his basement, Paul went one extra. He bought "FloodSafeTM Connectors...[which] automatically sense the rupture and shuts the water supply off when flow of water exceeds the design rate." These braided, flexible stainless steel beauties Paul bought cost a little over $20.
So what went wrong? Or rather, what went right? When the connectors were attached to the new washer, the service person unknowingly opened up the valve quickly, that caused the safety feature to engage -- and thus no water was allowed to the washer. According to the directions for the hoses, one should "slowly turn on water to full position." Once Paul and the Sears service man (from today) figured that out, everything worked like a charm. On the positive side, we know that our protection "against water damage due to burst, broken or ruptured water supply hoses or fittings" really works!
What the Auto-Shutoff Conector looks like...