I have a Kenmore top loading Washer (70 Series). Once the machine gets to the spin cycle the motor will kick on, the water will drain, but the machine won't spin. If you let it run it will continue with the cycle, and will enter the rinse cycle as normal, at the end of the wash cycle the clothes will be in a soaking heap at the bottom of the washer. If at any time during the spin cycle you open the lid, the motor will stop, you will hear a click, and once the lid is closed again the machine will spin as normal. What needs to be replaced?

You need a new timer. This is a whirlpool design and it has what is called a neutral pump-out where the motor runs and the pump pumps the water out but the tub doesn't spin. The timer is supposed to stop the motor for a minute or two after the neutral pump-out. And then when it starts again the transmission goes into spin. That's why if you open the lid the lid switch stops the motor and thus the transmission shifts to spin. For some reason the timer contacts that shut the motor of for this part of the cycle are not opening.