My Kenmore compact washer with dryer on top, will not go from the first wash-rinse-drain-spin cycle to the second rinse-drain-spin-off cycle.

Sounds like the brushes are struggling to get enough power to the motor to spin. Renew motor brushes

Check for an obstructed washer pump or drain hose.

Hi,
Try this link
http://www.acmehowto.com/howto/appliance/washer/diagwasher.php
pls rate my suggestion.......

level sensor needs cleaned or replace

CHANGE THE LID SWITCH

you both seem to have bad lid switches. A bad lid switch will prevent draining and spinning.

sounds as if you have a lid lick/door switch issue, the machine is not recognizing the door being closed and for safety reasons will not enter spin/drain.. open anc\d close lid a few times slowly, cam you hear a "clicking noise" whe njust about closed?? id assume not replace teh lidswitch

water pump blocked with nylon stuffing from old pillow.removed front panel from hinges under the lid. water pump at the right hand corner removed hose then removed 2 cups of nylon threads and stuffing forced into pumps small openings where it was compacted to a solid mass.

gabehart....sounds like belt is slipping. Replace it. The water pump is on a separate smaller motor so is not affected by the agitator/spin motor.

My Kenmore 98702 washer Fills and agitates as expected but stops at the end of cycle failing to drain or spin