When starting a new load of laundry, the washer begins to agitate before filling with water. Because the cycle seems to be 'off' the spin cycle does not seem to be removing the excess water from clothing. There is water in the bottom of the tub. The clothes do not seem to be getting clean either.

SOURCE: Loud clicking noise at spin cycle

It sounds like you have a motor coupling that has gone bad. Most of the Kenmore top loaders that I'm familiar with are direct drive machines. Which means, they use a motor coupling between the electric drive motor and transmission to run. If you are in the habit of doing heavy loads like comforters, blankets and jeans this can put a heavy burden on the motor coupler and wear it out faster. The coupler is designed to take the burden of the punishment in order to protect the transmission and drive motor and it is common for them to wear out. The coupler is fairly easy to replace and usually runs about $15. It is located inside the machine between the drive motor and transmission under the wash tub. You would have to remove the outside machine casing, the water pump and drive motor to get to it, though. Make sure the machine is unplugged before attempting any repairs involving removal of the drive motor. If you are not mechanically inclined, you may want to seek the aid of a repairman. I hope this helps.

SOURCE: Kenmore washer - water is emptying from tub but clothes are not spinning dry

replace door switch.If the computer thinks the door is open, it will not fast spin as a safety precaution. 

SOURCE: Washer spins but not enough to extract water from clothes or tub.

then its stuck drain sir

SOURCE: will not agitate to wash clothes but will spin fine

call a repair man. you cant fix this yourself

SOURCE: Kenmore Elite Top Load does not spin on spin cycle

Hi, If the inner tub has dropped down, you will need to change the block that holds the tub to the shaft. Remove the agitator cap and then use a 7/16" socket to remove the bolt holding the agitator in.
Lift the agitator out and look at the block holding the inner tub. There should be two slots with two tabs sticking up inside them. You will probably see metal shaving as well.
If this is what you see, please let me know and I can direct you on further repair.

Thanks
Vic