My Kenmore Series 80 top loader will not drain and begins the spin cycle then shuts down after a few spins depending on the water level. The machine can only be drained manually. There is no blockage of the drain hose.

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

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.

Your air pressure tube going to the water level switch is pinched or stopped up,OR, the water level switch is going bad.
Use this manual to access these parts and diagnose which is bad.

https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/f7e2147fa98b28cf85257122007475cb?OpenDocument

It does sound like a controller problem. Go to: SearsPartsDirect.com for parts diagrams and part numbers.

Bad/broken coupler/ http://www.davesrepair.com/DIYhelp/DIY285753.htm

Recommend contacting Kenmore directly for assistance Kenmore Customer Care Customer Service Information

Timer is defective. Your unit has a netural drain. When finished agitating, the shuts down and then starts up reversing to drain and spin. On the initial reverse start, the water drains without the transmission spinning. After a timed period 3-4 minutes, the timer is supposed to pause, stopping the motor for a few seconds. When the motor stops again, the transmission shift to the spin cycle and when the timer resumes power tothe motor it should spin. You are doing the same thing when you lift the lid...stopping the timer and then the tranny shifts and when you set the lid down, the washer spins. Replace the timer.......

Make sure all springs are still in their place tilt the machine back and look under it and you can see them. 2nd all legs must be level as well as the floor.

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.

where is the lint trap located