Hi all, thanks for the input!
What I forgot to mention is that the second motor that I wrote about in my previous post, the one that does not want to spin anymore, was a rebuilt one.
There is a manual about these motor revision made by some guys that explain in detail how to proceed. I did this, more than a year ago. All was fine until now as I'd explained.
There is no dust, no crud, nothing in there. I do not smell something burnt.
Yesterday evening (different time zone here

) I took the motor apart to see inside. Nothing to see, no damage on the shaft, windings, bearing etc.
I double checked the functionality by connecting the motor to another but exact same switch that these motors are hooked up to from factory, still did not work. Tried another, 3rd motor on that same switch, and that one spins.
So my guess is that it could be what james_s writes, the thermal fuse maybe?
I took my MM, and tested the wiring on it, the ones that run from coils to the switch, they seem ok to me.
But when I tested in Ohm mode, I got a reading on the yellow and brown wire of around 490 ohms, but the white and black got no result.
What does that mean? Can it be saved?