It was a box-office hit directed by John Gielgud and created turmoil on stage and off. Now, the 1964 Broadway staging has inspired The Motive and the Cue, a new play by Jack Thorne In 1964 Richard Burton played Hamlet on Broadway in a modern-dress production directed by John Gielgud. By commercial standards, it was a roaring success: it ran for 17 weeks, breaking a record previously held by Gielgud himself, and was p…