What is the model number of your unit, please?
Ok this sounds like either the motor has lost onre of its windings (not very likely, but posssible), or the timer is going bad.
The only way to determin which is by testing the system. To do that you will need the service manual.
What I have done is upload the service manual for your unit. It has all the diagnostic procedures and is clearly illustrated. You can get it by clicking here.
To download this file:
On the first page scroll down to the bottom and select "FREE"
On the next page enter the letters in the box and select "download"
Save the file to your hard drive and open it with a .pdf reader. I recommend FoxIt reader. (foxit.com) Its smaller than adobe and no spyware.If there is something in the manual that you do not understand just post here, and I will walk you through the proceedure.
They are DIY if you have a multimeter and know how to use it with a schematic. On a scale of 1-10 it is a solid 7. A good electrical diagnostics skill will be required.
Your unit is manufactured by whirlpool. The manual is the correct one.
The lid switch has nothing to do with a no drain situatilon. If the unit did drain but didnt spin then it would be the lid switch. The no drain situation would indicate that the motor did not turn in one direction. By providing inacurate information I gave you an incorrect diagnosis. Im sorry but I can only give you the information you request by the information you provide.
Best:regards; The Home Smithy