It certainly sounds like it, but you can check your starter motor by opening the engine bay, look at the lower right hand side of the bottom of the engine towards the back and you will see the starter motor.
It is easily identifed by a lever mechanism that lies from left to right which rests against what looks like a large button.
The lever is operated by the cable from the start lever.
Ensure the gears are set to neutral, get a long screwdriver or similar and press hard on the right hand end of the lever.
The starter motor should then operate, and as a temporary measure it is actually possible to start the engine using this method if you turn the ignition on.
If all is well you should consider changing the cable, which I am told (have never done it myself) is quite a fiddly job.
I seem to recall that the best way is to pull the new cable through by attaching it to the old one?
I am sure someone will correct me if I am wrong!
Good luck!