Are you saying the fan operates (low to hight) just fine in AC? That
does not make much sense, so I am assuming this is not the case.

Sounds like something is wrong in the switch because the 'off' position
is an open position under normal circumstances. Don't see how the fan's
resistor could possibly cause it to not turn off so that's not it.

Perhaps the common connection of the switch is permanently tied to one
of the contacts, maybe at the switch' connector.
In that case, switching to another setting may make a very small
difference in the speed of the fan motor, but you'll probably not
notice it.

Remco