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/index.action

Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.

Newer model Whirlpool / Kenmore washers use a Lid Switch as a safety device. Unless the switch senses that the lid on the washer is closed, the washer will neither

agitate nor spin.

Older models only used the switch during the spin cycle.

Try to bypass the Lid Switch by removing the Console and jumping the two outermost pins on the switch.

Following is a description of how to release the console for access to the pins.

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

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.

To bypass the switch, you only have to disconnect the power to the washer, tilt the console back, unplug the switch and using an short piece of insulated wire, jump

the two outermost contacts on the connector coming from the console and plug the washer back in.

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

With the jumper in place, try to re-start the washer.

If it works, the Lid Switch is a relatively inexpensive part.