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Replacement parts for WHIRLPOOL LGQ8857HQ0 | AppliancePartsPros.com

Have you cleaned the moisture sensor, Item 30 in Section 3.
If you did this with a damp rag try using some isopropyl alcohol, available at drug stores and a good all purpose solvent. Do not go crazy with it and let the fumes clear from the drum area before trying as it is flammable.

The way it works is that a small current flows between the sensor strips when moisture is present to act as a conductor. When the clothes are dry there is no conductor between the strips and the timer advances to off. Any dirt between the strips will cause the unit to think the clothes are still wet so the timer will not advance.

If this does nothing then the electronic control board could be toast, Item 22 in Section 1. Since this is fairly expensive I would try disconnecting the moisture sensor just to be sure that the sensor itself is not to blame.