Water from door dispenser taste and smell

We bought the refrigerator in Feb this year. In August we replaced the water filter inside. Since then we have had a foul taste and smell to the water coming from the door. It smells like mold or mildew. The ice tastes fine and when it melts there is not smell. We have replaced the tubing to the refrigerator, added an in line water filter before the refrigerator and replaced the holding tank inside. We do not run water through the door everyday, but use the ice all day. If at least 2 quarts is ran through it has no smell, but 2 hours later it is back. GE is telling us there is nothing that can be done and to have our water tested. Any suggestions would be great!