Washer fills but does not agitate or drain

try this
http://forum.appliancepartspros.com/washer-repair/345592-kenmore-90-series-washer-wont-agitate-spin.html
Kenmore 90 series washer won agitate or spin Appliance Repair Forum

Try eserviceinfo.com/index as per your 80 series. There are various downloads there that may help access the water level sensor which is most likely the problem.

Get a higher quality appliance

it sounds like the water valve is bad,the water valve level(sm. med. lg.)controls the water valce-mike

Screws holding the lid switch was broken. Had to replace lid switch.

you need to replace the agitator dogs, very simple. Go to www.shop.washermd.com and download the tutorial, thanks

defective motor coupling,,replace..onthejob

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.

if your washer will agitate when set to fill but not fill, then your pressure switch is bad.
also you may want to check and see if you are getting both hot and cold to your washer.