This may be caused by a pressure switch malfunction. This is the switch that is located behind the load level selector knob on the operator console. The following link explains what to look for:
http://www.fixya.com/support/r3575901-washer_overflowsI would recommend that you first check the small air hose that runs from the bottom right hand side of the wash tub to the pressure swtich. Open the operator console and check the air hose connection on the pressure switch. If this hose has come loose from the pressure switch, the pressure switch will not sense the pressure differential coming from the wash tub as the unit fills. Also, if the air hose is cracked, ripped, split, or clogged somewhere, you will get the same symptoms.
For better access to all internal components of the washer, you have to remove the exterior washer case to inspect. The following link explains how:
http://www.fixya.com/support/r3631789-washer_case_removal_whirlpool_top
If everything appears to be intact and the air dome hose is connected properly and not leaking, replace the pressure switch. The part number for the model you have listed is 8577842.
Replacement parts (if required) can be purchased at any of the following websites:
searspartsdirect.com
pcappliancerepair.com
appliancepartspros.com
repairclinic.com
All these sites are reputable and offer great service with competitive pricing, so shop and compare. The first three sites I listed also include helpful exploded view parts diagrams to assist you in locating and properly identifying the parts you need.
If you need further assistance, please post back and let me know. I hope this helps lead you in the right direction.