This is going to have to be a bit generic, as I don't recognise your model number, so can't be sure what sort of motor you're dealing with.
If you haven't got a multimeter, suggest you buy yourself one (it needn't be expensive, and once you have it, you'll find it's useful for all sorts of jobs).
With the machine disconnected from the electrical supply, unplug the cable that connects the motor to the rest of the machine. You may also find taking the motor right out gives you better access.
Carefully remove and inspect the brushes. Make sure that they haven't worn to the point where the springs are no longer pushing them against the commutator. After refitting them, but before reconnecting their wires, measure the resistance between them. Expect it to be in the order of tens of ohms, and to remain in that range as you slowly turn the motor.
Look for a pair of wires going into the windings on the body of the motor, and measure the resistance between these. Again, expect it to be of the order of tens of ohms.
If that all looks good, and you can't see anything obviously wrong with any of the wiring, trace the motor wiring back and see where it goes.
If you find a starter capacitor (will look something like the item pictured on
http://www.tdspares.co.uk/proddetail.asp... you might try replacing it on spec - it's cheap enough for you to be able to afford to get it wrong.
Hopefully that'll get you started.
A.