You have not given much information to go on to narrow it down to any specific system or part. From what you have given us, here are some things that could cause the problem:
1.)Timer - If it isn't telling the motor to turn in the proper direction and speed or briefly pause after the pump out, this washer will not spin.
2.) Lid Switch - This is a safety device. During spin cycles it is put in series between the timer and the motor to prevent user harm. It allows the motor to get electricity when the lid is down and takes it away when the lid is up.
3.) Out of Balance Switch - A safety device. During spin cycles it is put in series between the timer and the motor to prevent harm to the machine. It allows the motor to get electricity when the basket assembly is in the proper plane and takes it away when the basket assembly is off kilter. Not found on all models of this series, only the more expensive models.
4.) Spin Clutch Assembly - This is the interface between the spin tube and transmission that causes the spin tube to spin.
5) Drive Block - This is what attaches the basket to the spin tube.
6.) Centrifugal Switch on the Motor - This is the interface between the wiring harness and the motor. It tells the motor which set of windings to use.
7.) Motor - This has a multi-speed 2 direction motor that incorporates multiple windings to achieve some of it's functions.
8.) Wiring Harness - If there is an unintentional break between the timer and the motor.
Please tell us more about what this washer is doing or not doing.
Is it pumping out water? Is the motor running at all during spin? Is the motor running but the basket is not turning? Have you visually seen the agitator working?