All Kenmore front load washers have belts, but these almost never are the cause of a problem. You can feel the belt by taking off the font access panel and reaching way back to the motor and feel for the belt. Do this with the unit unglugged, for your safety. But what is really telling in your post is that you hear something going on in the unit, and figuring out what you hear is going to be key to fixing it. If the problem were a broken belt, you probably wouldn't hear anything, because front load washer motors not under strain of a belt are practically silent. I bet what you hear is the pump.
I am going to take a guess that you have a Kenmore FL washer with model that starts with 417. If washer is filled with water and won't drain where it is supposed to spin, then deal with the reason that it isn't draining: the pump. FL washers won't spin until they drain. If it will drain, and it will "agitate" (tumble slowly) during wash cycle but it won't spin in the spin cycle, then it is probably the door switch. If it will neither agitate nor spin, then it is probably the motor controller that is your problem.