Kenmore Trio Ice Build Up and Leaking

My Kenmore Trio is a little older and doesn't have a Duckbill. Bottom of the freezer has ice build up and then leaks all over the kitchen floor. We took off the back of the frig and we just have a tube going down to the drip pan and it's clear, nothing clogging up the tube. I went to the Sears website and asked them what to do. They pretty much told me to unplug the unit and let the ice melt or taking off the plastic back inside the freezer and melting the ice and unclogging the tube inside there. Of course that is just a temporary fix and doesn't explain WHY it's happening and what we can do to stop it. So of course we have a ruined kitchen floor and who knows how much mold is growing under our tile squares. I understand it's "just" some peel and stick tile, but it wasn't cheap for us to do our whole kitchen and now it's ruined and we have a refrigerator that will ruin any floor we put down because Sears refuses to stand behind their products and make it right!