Why is my kenmore washer agitator (the top part) not working?

If you are talking about the large plastic center "screw" of the agitator not pulling the clothes down, there are 4 small cogs under the center cap that are worn. You'll have to remove the center small bolt in the center holding the agitator to the trans shaft, lift off the agitator and take it apart. Pick up a new set of cogs and replace then then reassemble everything you took apart.