A 1973 motor certainly has had time to wear out a starter, but it is pretty unlikely since those motors crank so easily. If it is cranking slowly, the most likely reason would be high resistance in the starting circuit (cables). Take them off and scrape/wire brush everything shiny bright. And of course make sure the cables aren't corroded half way through or something like that.
EDIT: And make sure that "fully charged" battery doesn't have a dead cell or something. Have it load tested. Many or most battery stores will do that for free.