Open the appliance far enough so that the output leads from the controller board are visible leading to the motor. Determine that a Triac is present on the PC board.

Using a VOM, test for voltage across the motor on the output of the controller board. The voltage should range from about the same as the voltage at the wall socket at its maximum and zero when the device is turned off. From "off" to maximum the voltage should increase with increase in the position of the speed selector.

If the BT136 triac is present on the PC board AND there is no voltage present across the motor connections in any any position of the selector... The problem is almost always a problem with the triac.