No spin cycle

387780 does not seem to be a valid model number.
If you can locate the model number enter it here at sears Parts Direct.
Parts for Brands Craftsman GE Kenmore Whirlpool and more

Link to videos about washer not spinning.
top loader kenmore washer won spin YouTube

check brushes on motor

Hey! if someone else needs the manual, it can be found under this link: https://gdgtpreview.com/2018/09/kenmore-80-series-washer-manual

they are called dogs part#80040

This is a problem in your transmission. Not Good!

You may need to replace the motor coupling between the pump and motor...

Check for buildup of detergent/foaming while washing. Check for oil leaks around the clutch area. Could also be the clutch lining is worn out. Replacement parts kit includes all parts

Manually move the timer to the SPIN mode and turn it on.
If nothing happens, replace the lid switch.
With a model number I could be more specific.

If you are getting no water spray during the rinse cycle that would cause the soapy clothes issue.

Are you getting cold water during the wash/rinse cycles? If you have the machine set to warm/warm you may only be getting hot water while the final spin is calling for cold.

If you have cold water available then the timer is not calling for the water spray. The problem is either in the mixing valve or the timer.

you have something gotten into your pump ,,, it trys to drain and spin but overloads the motor and shuts down till the motor switch resets .... remove the pump and take out whatever gotten in it and if that not possable replace the pump.