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Replacement parts for KENMORE 66516912001 | AppliancePartsPros.com

Here is the tech sheet, see attachment.

It could be that the board you received is no good but is uncommon for this to happen and even more uncommon for exactly the same fault to show up on both boards.

I doubt it is the console as it is a matrix type so the keys work as sets therefore it does not make sense that they would all go down at one time.
There is a caveat on this and that would be if a diode shorted and is pulling down the keypad power supply voltage.
I would check it with a meter doing both forward and reverse biasing of the diodes.

I think you may have just missed something.
I am assuming that you are measuring voltage from the Neutral and not just earth ground (the frame).
On the switch do you see voltage at both sides of it when it is closed?

When you measure the parts for continuity did you disconnect one side of the part? This ensures that you do not read an alternate/parallel circuit path.