With that combo of symptoms, I'd suspect a problem with the damper control assembly. When it fails, it often gets stuck in the open position, causing a constant stream of frigid air to rush in. This explains why your produce is freezing, and it also explains the water dispenser issue, as that frigid air blows directly onto the water line, freezing the water inside. Before you call a pro, try checking it yourself. The damper is typically in the back of the fresh food section, behind a panel. Look for frost buildup around the assembly, which would confirm if it's stuck open. If it is, a replacement damper is what you'll need.
