Check out the carbon brushes in the motor. Theyre graphite blocks which transfer mains power to the copper segments of the motor -Theyre probably worn down. They're quite cheap parts and easy to replace. Power off, remove the back cover and locate the motor. May help if the machine is tilted at an angle or laid on its side. The brushes are at the other end of the motor from the drive pulley. The holders are plastic or bakelite and are generally held in with screws or plastic clips. Also, look at the copper segments they run on to check for burning or pitting. If the segments are burnt or damaged you need a replacement motor or a replacement armature (motor part) if you can source one. Occasionally may be a fault in the motor drive circuit board - in which case replacement of board only real option.
Other possible causes of spin problems: Faulty pressure switch - machine "thinks" the drum is still full of water so wont enter the spin cycle. An easy way to check is to remove the hose connected to the pressure switch and listen for a click. Spin problems may also be caused if the machine reckons the load is out of balance, rearrange the load. If problem persists could possibly be a fault in the out of balance detector switch or the suspension and damping system.
Repair and service your own washing machine. Check out www.2ndwave.co.uk/manual.html
dannyboy, November 2008