so, what I did by connecting L1 (black on timer) to S (purple) should power the motor and make it run?
Yes it should have run.
As long as you are sure there is L1 to Neutral power then I would replace the motor.
Just strange that there is not hum/buzz when at least one winding measures OK.
Looks like the motor is around $175.00 so unless the unit is in very good shape I would scrap it.