Just replaced timer and bypassed safety lid...

First, see the Sears parts site for your washer:

http://www.searspartsdirect.com/partsdirect/getModel!retrieve.pd?modelNumber=110.22722101

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

If you cannot hear the motor trying to turn the pump, (but the washer will agitate) the problem initially points the Timer, or the Lid Switch.

Since you've already replaced both, the problem points to the "Neutral Drain Assembly" in the transmission,

This is a Whirlpool PDF on how these washers operate. It has a diagram on jumping the switch as well as a detailed section on how the transmission works.

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

It also has a troubleshooting guide.

Following is a description of how to gain access to the console and how to remove the cabinet if necessary.

http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=131&osCsid=913ba652cd504fb162f87d892bcb427b

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.

Following is the Whirlpool parts PDF for their commercial version washers although the consumer models use the same transmission parts.

With ours,we 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.