How can I fix my LEC fridge/freezer?

I have a 'frost-free' LEC fridge/freezer. It is about five years old, and has been completely reliable until now. The motor is working, but the moisture-draining channel at the back of the fridge compartment is continually full of water, and is not seeming to drain properly. It appears to have spilled over onto the base of the fridge part, and then freezing on the surface. After clearing it, it occurs again within a few hours. Any advice?