I don't know anything about your make or model, but take a look at my postings, (at the end of this ramble), on what sounds like a similar problem to yours and how I fixed it. (Mine is an 'old' Zanussi)
I agree with Tony if your motor has brushes (grahite blocks with pass the current to the motor's rotor windings) you should check/change them. Mine, although 13 years old does NOT have brushes as it is an induction motor.
Does yours rinse ok or does it struggle with a heavy load in that it fills with clean water, doesn't do much if any turning of the drum, drains ok prior to attempting and failing to initiate a spin?
I hope this helps.
(PS take care if you 'accidentally' happen to be 'experimenting' with the covers off! - Something of course that you shouldn't do.
Remember that there are mains voltages and you don't want to stand in the path of the motor/belt/drum pulley if for any reason it happens to be spinning with the covers off - because if anything 'lets go' at around 1000 rpm you do not want to get in its way!)
http://www.howtomendit.com/answers.php?id=21937
Jonathan Leak, March 2006