Welcome to the site. It's always better to start a new thread with a new question. If it is frozen, that would indicate other problems. More likely a vent problem, for the drain to work proberly there has to be water behind the water. Without venting the water will either drain really slow or suck the water out of the trap. The vent should go out thru the roof and covered with snow. If that might be the problem and getting to the roof is not possible, adding a cheeter valve to allow air in the system is a cheap and easy fix. It allows air in the system and then reseals to stop gasses from coming into the house.
See the white thing in the back above the level of the trap.