Why does the spin cycle not start

As Mayer said #1 cause is lid switch. i love vintage "repairable " washers. I recently had a weird cause of no spin on an '80s GE. I put a hamper of dirty cloths on top of the lid and it flexed the center of the lid down causing the lid switch pin to pull up enough to prevent spin. I tested the switch and it was all good then I noticed the lid was still pressed in. I gave it a bump and it popped back to slightly domed and tada everything worked. Over the years I've just cut the wires at the switch and added a wire nut to "fix" a bad switch or snapped lid switch pin. Don't do this at home.

When I was a kid that switch didn't exist and we were smart enough to not reach down into a whirling 20 # load of cloths. Might just wrench your arm clean off. Nowadays humans aren't that smart so machines have to have loads of safety switches that often fail. Many new machines won't let you open the lid to add soap or laundry as the machine fills. That's to protect us from the hot water or possible drowning.

On a grand old '83 the next likely cause for no spin could be bad timer. My machine won't run on high speed in regular and perm press due to burned timer contacts. I now have to do all my washing on gentle. Looking for an affordable gently used or dusty new timer. There is no computer board or sensors. The safety switch just cuts the power to the spin circuit. One last cause of no spin is a bad water level switch. When the pump turns on and the water is mostly out of the drum the water level switch closes and sends spin circuit power to the motor and clutch to engage spin instead of agitate. Which leads to: if the spin doesn't work but every thing else does the transmission and or clutch may be bad. Washer drive train repairs are advanced repairs. But on those old workhorses drive train failure is very rare.