The tub never starts to spin when it hits spin cycle.

If your washer functions when the door is shut it cannot be a door problem. The likely thing here is you may have a drain problem....your drain oulet filter (or out pump) could be blocked. This requires cleaning; when the washer goes thru all the functions except spin it is most likely your drain is clogged. Aft u have cleaned the filter & pump check by a small spin. Before you attempt, wall socket off & keep bucket handy to collect water.