Update: I tried to take out the top freezer drawers, but failed miserably. I started by taking out 2 1/4" screws on the left and right side of the freezer. I pulled the left top drawer all the way out. I pushed in the 4 tabs and lifted up, but the rail assembly refused to come out. Next, I went to the back of the refrigerator, took off the old rubber drip plug and stuck a coat hanger in the small hole. I was able to go up about an inch from the hole and it hit something solid (probably ice). Not knowing what else to do, I just installed the new drip drain and put everything back.
Is there a way I can quickly thaw the ice buildup from behind the refrigerator?