Somewhere in the unit is a coil of either copper or plastic line, normally on the refrigerator side. This is where the water sits and gets cooled and should be protected from products inside. Sometimes something can get pressed against it and pinch or crimp it. Here are a few 'how to' sites that may help.
http://fixitnow.com/wp/2009/01/25/no...-refrigerator/
http://products.geappliances.com/app...ontentId=16239
http://www.partselect.com/Repair/Ref...pensing-Water/
http://bustedrefrigerator.com/ge-ref...er-not-working