Kenmore top loader

Hi
I see your having the washing machine won't spin problem. The first thing I would sugest is to disconect the AC power from the machine. The next step is to remove the front panel from the machine. Look at the top lid for a plastic tip that fits into a keyhole in frame. Underneath there there's a safty switch. This switch is designed to stop the machine from spinning if the lid is open. Sometimes the switch gets corroded over the years. It may have to be replaced or adjusted to align with the plastic tip whin the lid is closed. The black thing hanging down from the motor you described could just be some electrical tape the manufacture uses the bundle the wires from the motor. Some manufactures use a spring to keep the wires from the motor from interfering with any moving parts.

Hope this helps.