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Replacement parts for KENMORE 66513213K901 | AppliancePartsPros.com

Sears will have parts breakdown diagrams.

The unit is made by Whirlpool.

Open the unit right after it fills to see how much water is in it.
Most units fill to just under or just over the heating element. Not sure which on this unit.

If the water seems low add a couple quarts of hot water to the tub.
Just be careful to not overfill it.
Then shut the door and give it a try.
By "jets", I am assuming you mean the wash arms.
If they now spin and spray OK, then the most likely cause is a partially plugged screen filter on the input side of the fill valve.

Remove the valve from the unit and clean/check the filter.
Do not permanently remove it from the valve as it is there to keep crud out of the valve which could hold it open and cause a flood.

If it still does not fill correctly I would replace the fill valve.

PS: Be sure to shut off the power and the water supply to the unit. Have paper towels etc. handy to wipe up any spilled water. Get a small pan/bowl etc. that will fit under the valve then loosen the input water line let it drip into the container emptying it as necessary. This will minimize the amount of water spilled.