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Replacement parts for Kenmore 66513443K900 | AppliancePartsPros.com
See the attachment for the tech sheet.
You will notice in the keyboard pin-out that the light was ans delay have P1-11 as a common, also the start uses this line.
I would do the following first.
Connector Cleaning / Checking
Unplug the unit
Open it up
Remove the ribbon cable from the keypad to the control board at the control board.
Clean the edge connector.
If it is the type where there is not a connector just the insulation is removed, it can be cleaned with a pencil eraser. Do not use an ink eraser as it is too abrasive.
Check the tracks in the ribbon cable for hairline cracks. A magnifying glass helps here.
Would not hurt to clean the connector on the board. Use electronics contact cleaner or isopropyl alcohol and a tooth brush. Be gentle and do not reconnect till all the solvent evaporates.
Reconnect everything and give it a try.
If that does nothing then check the keypad with a meter.
If you find a fault replace the control panel (keypad)
If OK replace the control board as it can also cause this.
Still a bit of a crap shoot but your odds are better.