Kenmore model 110 20702 991 will run until the spin cycle and not spin you can open the lid and reset timer to spin cycle and it will begin to spin. relaced lid switch still does the exact same thing

This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.

First, see the Sears parts site for your washer:

http://www.searspartsdirect.com/partsdirect/getModel!retrieve.pd?modelNumber=110.20702991&pathTaken=partSearch


and you'll see a list of major sub-components with diagrams and parts.


The Kenmore / Whirlpool top load uses a reversing motor to initiate the pump for draining and the transmission to spin.

If it will drain but won't spin the problem is likely in the transmission. "Neutral Drain Assembly".

See the Whirlpool / Kenmore Service manual for top load direct drive washers.

WHIRLPOOL INST AND MAINTENANCE INCLUDING HOW TRANSMISSION WORKS

https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/f7e2147fa98b28cf85257122007475cb/$FILE/L-55.pdf


WHIRLPOOL TRANSMISSION DESCRIPTION AND SPRINGS

https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/2550f737b3129b0c85256b0600504738/$FILE/787772%20%234.pdf


Those cams/gears etc. in that assembly keep the washer from spinning until all of the water is pumped out and then go into spin mode.

When ours had a similar problem,(wouldn't spin unless we opened and closed the lid a couple of times) we looked at the transmission parts list (available on a number of sites) and on the Whirlpool site (Whirlpool makes Kenmore) and noticed that the one of the cams in the neutral assembly which is supposed to have a small spring, didn't on ours when we tore the transmission apart again

http://shared.whirlpoolcorp.com/assets/pdfs/literature/Repair%20Part%20List%20-%20W10114743.pdf

Found the part number for a kit (Whirlpool part number 388253 Neutral Assembly) for $15.00 and replaced the cams and gears.

In order to get the transmission out, you have to remove the cabinet, the fabric dispenser and both agitators. The top agitator uses a plastic 1/2" drive bolt (a 1/2" socket extension works well).

You don't have to remove the drum.

http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=137

Lay the machine down (after disconnecting power and hoses, remove the pump (two clips), the motor (two screws hold two clips on the motor), lift and set the motor aside.

Remove two 1/2 inch bolts for the motor mounting plate and three 1/2 inch bolts for the transmission.

Pull the transmission, remove the clutch (there is a spring clip that holds the clutch on the main agitator shaft), remove the 8 screws carefully the transmission holds 14 - 15Oz of oil, remove the clip holding the main spin gear on and check the plastic cams.

If the cam that should have a spring doesn't, or the others look damaged, or the main spin gear is damaged the washer won't go into spin mode.

If that's the problem, install a Neutral drain kit, put everything back together carefully and the problem may be solved.

As an aside, fixing ours cost less than $30 including 80-90 weight gear oil vs. $170 for a new transmission.