Buzzing noise but washer will not run - Kenmore 20722

Her you'll find your answer..
http://www.appliancerepair.net/washing-machines-forward.html

You need to check the drain pump / filter. Here is a link that should help http://appliancehelponline.com/washerdrainpump.html

I think that the draining pump is faulty,or filter is overload.

The lock solenoid on the door latch assembly may be hanging up or just noisey. If washer starts and runs then all is ok. If washer wont start, just buzzes, then door latch assembly may have to be changed.

i think the problem that you have is one of the electric coils from the entrance valve from water. Check if there the vibration comes from there.

from your description, i would guess that the drive coupling has stripped or broken. relatively inexpensive fix. not a job for the inexperienced do-it-yourselfer

Most noises from a washing machine occur during the spin cycle. If you hear loud thumping during the spin, the load of clothes may have become unbalanced. Stop the washer and redistribute the clothes, then re-start it. Repeat these steps if necessary. 
click the link http://www.repairclinic.com/0088_11_1.asp#Level1_5

Check the water pump for an obstruction in the chamber area, your pump may be sticking and that will cause the buzzing sound. The water pump runs during the fill portion of the cycle on several of the selected wash cycles to recirculate the water.

Is your water on ??if yes than you may have a bad timer.

Try some anti-sqeek or soap on your washer belt.