"Cutoff" means that the base current is biased in such a way that the
collector-emitter current is cut off ... zero current through the transistor.
"Saturation" means that the base current is biased in such a way that
the collector-emitter current is the most it can be ... max possible
current through the transistor.
-- In order for the motor to run, there has to be some emitter current.
-- The transistor is a current amplifier. In order to get any emitter current,
you'll need a little bit of base current.
-- The way the circuit is built, there's no way to get any base current.
Grounding it doesn't do anything.
-- Leave the switch where it is. But disconnect the resistor from
ground, and connect it instead to the top of the battery (the collector
terminal is a convenient place). Then, when the switch is closed, the
base gets some current from the battery through the resistor, big current
appears through the collector-emitter, and the motor spins up.
