If there is some rotation then it suggests it's not a logic fault so it's likely to be:-
1> slipping drive to the drum - if it's belt drive I'd expect to hear a squealing noise (like cars on a cold winter's morning with all the electrical stuff switched on the alternator belt slips under the load and makes a squealing noise).
If this is the case then replace the belt.
2> motor is losing torque; caused by worn brushes or faulty capacitor. Depending on your machine the motor may or may not have carbon brushes. These carry electrical current to the bit of the motor that actually turns. Because they rub on the commutator (that, (low friction), + conductivity is why graphite is used) they get worn and no longer make a good enough contact onto the rotor to transfer the current needed when that motor has to spin a heavy load.
Some motors do not have these brushes.
( instead they use a controller to vary the stator's magnetic field inducing an interacting field in the rotor which cause rotation.)
For these (brushless motors) you can try changing the 'starter' capacitor - it worked on my Zanussi; see my posts below.
If the symptons are that the drum visibly attempts to turn but doesn't manage to complete many rotations and in front loaders it 'stalls' as the load(water+clothes) gets to the 11 o'clock or 2 o'clock postions then look at my posts:-
http://www.howtomendit.com/answers.php?id=33527
JonL
June 2006