Thanks to all for the input.
Turns-out that this device is actually a surge protector !

I was able to find the wiring diagram of the dishwasher,
and while there is no diagram for the control board itself,
I was able to figure-out that the device is basically connected
across the 120VAC power line mains once the door switches
are closed.

Thus, the melted VR300 'thermistor' is actually a surge protector.
Thankfully I had not tried the thermistor replacement trick yet.

I did further tests on that board, and discovered that a few diodes
including at least one zener are either short or opened...
Plus a 2N3904 transistor is short too.
I guess the surge protector did not quite protect the rest of the
circuit.
I wonder if this occured during a storm (I was not at home when the
dishwasher became defective).

Given that there are too many bad parts on the board, plus there
may be more chips zapped too, and given my limited spare time
(and my wife threatening to call a serviceman!),
I will have to bite the bullet and buy the replacement board
Darn, I thought it was going to be a simple single bad part...

Thanks again for all the input and interesting discussions,

Regards,
- Sylvain