That could be the motor coupler. It could also be the transmission. It is pretty easy to fix. I recently worked on my brother's washer: If you need further help, reach me via phone at https://www.6ya.com/expert/dan_73bbd84fe1d95b61
When this machine is not spinning, the water should still be able to drain, as the motor drives the pump on the same shaft as the coupler for the tranny. Set to the spin setting and depress the lid switch, if the water still does not drain, you may have something stuck in your pump, which would also lock the motor shaft and not allow it to spin or agitate. If the water does drain, check the motor coupler, which is located between the motor and transmission, if broken, the motor will run but there is no drive to the transmission. Hope this helps...
first thing to check would be to see if the lid switch went bad simply by clicking the switch and listening or takeing a wire and unplugging the actual switch and jumping with the wire from the first connection spot to the third this by passes the lid switch try to start the unit when this is achieved.if the unit still does not turn on here is a video of how to open the unit in the begining of this video http://www.youtube.com/user/RepairClinic?v=9K1KHEogf3c&feature=pyv&ad=5453897861&kw=whirlpool%20coupler&gclid=CNmDuYeGzagCFUff4AodWDxRhA
after you get the cabinet off as to the clicking noise if its during the spin cycle then you would follow through the entire video to replace the drive coupler this is step by step instruction in this video of how to check the drive coupler and how to replace if you have any further questions message me back and please remember to rank how this opinion has helped in your appliance situation also if you find the drive coupler is not broken message me back as well and I will diagnose your issue further Thanks again Rick
btw drive coupler goes for about 10-14 dollars and you can find it at this place click here http://www.allbrandonline.com/
Go to the link below and enter your model number in the search window there.
Sears has thousands of parts lists and line drawing illustrations that can aid in finding the reset button if present or any other part you may want to locate or replace.
Sears PartsDirect
BTW, it does not have to be a Kenmore or Sears-branded appliance. They have many others as well.