A bit more detail would be useful. Like how have you arrived at the decision that it is the starter motor?
If you are happy that it works off the car, but not on, then you have to check the electrical supply and earth.
As Fingers says, a jump lead from battery negative to gearbox will by-pass the normal earth wire. If it then works, this shows that the earth wire connections need cleaning, or the wire is broken.
At the starter you have two connections. A fat one, for the cable direct from the battery positive. This goes to the solenoid and is live all the time. There is then a short fat one from the solenoid into the starter, this is part of the starter. This is only live when the solenoid operates.
There is also a small connector. This becomes live when you turn the ignition switch to start the car. A current is put to the solenoid, which engages the pinion with the flywheel ring gear and makes the contact inside the solenoid to connect the fat wires together to make the starter turn. You can test that current is getting there by disconnecting it from the starter and connecting a test bulb from it to earth. It should light when you operate the key. Can also be done with a voltmeter.
Off the car, applying voltage to the small connector will often turn the motor, as this connection earths through the motor windings, but you are not testing it under load.
So first, is there 12v to the small connector from the switch.
If there is, does it cause the solenoid to operate properly.
When that happens, do you get 12v at the output from the solenoid to the starter.
Could be an ignition switch fault!
Sorry, that's a bit long-winded. Squeak if it does not make sense.
