Edit - removed multiple copies

Edit: I don't know why this posted multiple times---sorry.

If it truly isn't spinning during only one cycle that is probably the timer.

Here's a simple test, it sounds worse when written than it will be in reality; you just will take 15 minutes of standing there.

The lid has a pin that pushes through a hole in the cabinet to depress the lid switch. That hole is on the right side of where the lid sits in the top. You can use a pencil or other slim object to push that switch (it'll click when the switch closes) and trick it into allowing you to run it with the lid open. Let it run normally through a cycle that seems to not spin out. When it reaches rinse and has filled and begun agitating, open the lid and manually push that lid switch so it'll move on to drain and spin as if the lid is closed. It'll take a few minutes of holding it but you want to let it progress as the cycle normally does.

After a few minutes of agitation, the timer should end the agitation part and reverse the motor to run neutral drain prior to spinning in order to empty the machine. Ideally if you continue to hold that switch down a minute or 2 later the timer should briefly kill the motor. Upon restarting it should start spinning. If you release the switch briefly during neutral drain it'll also start spinning when you depress it again.

Caveat - It may not do neutral drain properly and begin spinning early, that isn't a major problem in itself as long as it isn't sloshing water over the top. It's extra wear on the clutch but not worth addressing on it's own as it means a new gearcase.

If it doesn't progress into spin at all and just ends after 6-8 minutes of neutral drain (when it should have been spinning) you have a bad timer that isn't opening the motor circuit to flip the gearcase into spin. If it spins lazily you probably have a bad clutch. The timer is easy to change but the clutch is cheaper.

If permanent press works and you do not want to spend $ on it just use that cycle. It spins slower I think but otherwise you wont notice much difference.