Kenmore Mod 110 24632300 won't drain

First, see the Sears parts site for your washer:

http://www.searspartsdirect.com/partsdirect/getModel!retrieve.pd?modelNumber=110+24632300

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

I'm assuming that it will spin.

See the section for the Pump, Motor and gearcase and the basket and tub assembly's

I'd pull the cabinet in order to get to the hoses going to and from the pump first.

See the following:

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

If the hoses are fine, check the shaft from the motor to the pump and check inside the pump to make sure the inlet and outlet aren't blocked.

As an aside, see the following Whirlpool Service Manual for top load direct drive washers.

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