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By your description, it does sound like the starter motor.
I would get a long screwdriver etc to listen the starter while you get a friend to start the engine.
Does it do it every time?
Unusual at that age, has it had a lot of starter motor use in it's life so far?
I hope my advice has helped you today.
How did you go with your problem?
I hope my advice has been of assistance to you.