You will see as you dismantle the carb what needs cleaning( I am a FIRM believer in soaking versus spraying) and what shouldn't , I.E., any diaphram. 9 times out of 10 it's the jets that "varnish" from old gas & fuel can not get through.
If you are mechanically inclined, the starter is pretty easy to figure out, especially if you've got the manual. Take it apart & you will most likely seewhat the problem is. It's usually parts that need cleaning & lubricating, or the flywheel teeth are ground down so badly that the smaller gear no longer is able to spin it(my flywheel had worn gear teeth that looked fairly bad when I first opened it up, but after some tlc, the starter works 98%, only slipping once in a blue moon), but more than likely your problem isn't the flywheel.
Good luck, and post up your results, Lefty.