The machine appears to work with the exception of the spin cycle. Reading here clues appear to point to "off balance" ("someone" washed some quilts in it, so that would make sense;) - but how do you reset the balance or more to the point check it? I have had the top off - and the four hanging wires holding the drum "appear" to be OK, no idea what I am looking for!
it sounds like you have a failure with your solenoid motor, remove rear panel set onto spin cycle and observe that the the lever pulling device is doing its job note;will happen when
water has empted, good luck.
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Try fixfault.com to fix washing machines.