Kenmore 80 series. doesnt pump water out; wont spin

Check in this order: belt, water pump, motor, drum shaft/bearing. Most of the parts will be either under the unit or inside. Most units require popping the top up in the front and removing the front panel.

sounds like it needs a new belt

you will need lid switch 285671.. whirlpoolpartssurplus.com

drain pump is trying to drain. maybe have something in pump

POST ME THE MODEL NUMBER. AND ALWAYS POST MODEL NUMBERS WHEN NEEDING ASSISTANCE PLEASE:)))

sounds like the coupler that connects the motor to the transmission is going bad.  A $20 part

Check the coupling/transmission.

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unless your washer is over 20 years old, then it wont have a belt. the temperature of the water wont have anything to do with it spinning or not.
need to know if it agitates or drains and just wont spin.
if it agitates but no spin or drain, then you have a bad lid switch.
if it wont agitate or spin, but will drain, then you have a broken drive coupling.

Mrquest
If it is draining the water then the motor is running. ou most likely have a broken motor coupler between the motor and gearcase.

Remove the two screws that hold the console to the cabinet and flip the console back.
Remove the two clips that hold the cabinet to the rear panel of the washer and unplug the lid switch harness. The cabinet will tilt forward and slide off.
Remove the clips holding the water pump and move it to the side.
Unplug the wires from the motor and remove the clips holding it.
You will see the motor coupler.
Make sure you can turn the gearcase shaft with a pair of pliers so it is not locked up.
Post back with the complete model number from the washer if you need further help.
Thanks, Mike