Hugo

In 1931, 12-year-old Hugo Cabret (Asa Butterfield) lives in Paris with his father (Jude Law), a widowed, but kind clockmaker who also works at a museum. One day his father finds a broken automaton, a mechanical man designed to write with a pen, at the museum, and he and Hugo try to repair it, his father documenting the automaton in a notebook. When his father is killed by a fire at the museum, Hugo is forced to live with his resentful, alcoholic uncle Claude (Ray Winstone), and made to learn how to maintain the clocks at the railway station of Gare Montparnasse. When Claude goes missing for several days, Hugo continues to maintain the clocks, fearing that he would be sent away as an orphan by the vindictive Station Inspector Gustave (Sacha Baron Cohen) if Claude's absence is discovered. Hugo attempts to repair the automaton with stolen parts, believing it contains a message from his father, but the machine still requires a heart-shaped key that his father could not find.
Hugo is caught when stealing from the toy store owner Georges (Ben Kingsley), who looks through his father's notebook and threatens to destroy it. Hugo encounters Georges' goddaughter Isabelle (ChloÃ« Grace Moretz) who offers to help get the notebook back. Hugo learns Georges has forbidden Isabelle from going to the cinema, and introduces the medium to her as his father had done for him. As their friendship grows, he shows her the automaton, and is surprised when Isabelle reveals she wears the key as a necklace given to her by Georges. When started, the machine draws out a scene that Hugo recognizes from his father's description of the film A Trip to the Moon. Isabelle identifies the signature, that of a "Georges MÃ©liÃ¨s", as her godfather. She sneaks Hugo into her home, where they find a hidden cache of more imaginative drawings of MÃ©liÃ¨s, but are caught by Georges, who banishes Hugo from his home.
Hugo and Isabelle go to the Film Academy Library and find a book about the history of cinema that praises MÃ©liÃ¨s' contributions. They meet the book's author, RenÃ© Tabard (Michael Stuhlbarg), a film expert who is surprised to hear that MÃ©liÃ¨s may still be alive, as he had disappeared after World War I along with nearly all copies of his films. Excited at the chance to meet him, RenÃ© agrees to meet Isabelle and Hugo at Georges' home to show his copy of A Trip to the Moon, hoping it will invigorate Georges. On the scheduled night, Georges' wife Jeanne (Helen McCrory) tries to turn them away, but RenÃ© compliments Jeanne as Jeanne d'Alcy, an actress in many of MÃ©liÃ¨s' films, and she allows them to continue. As the film plays, Georges threatens to send them away, but Jeanne convinces him to cherish his accomplishments rather than regret his lost dream. Georges recounts that as a stage magician, he had been fascinated by motion pictures and used the medium to create imaginative works through his Star Film Company, but was forced into bankruptcy following the War, closing his studio and selling his films to be turned into raw materials. He laments that even an automaton he made that he donated to a museum was lost. Hugo recognizes this is the same automaton he has, and races to the station to retrieve it. He is caught by Gustave, who has learned that Claude's body was found some time ago, and threatens to take Hugo to the orphanage. Georges arrives and tells Gustave that he will now see to Hugo, adopting him as his son.
Some time later, Georges is named a professor at the Film Academy, and is paid tribute through a showcase of his films recovered by RenÃ©. Hugo joins in with his new family as they celebrate, while Isabelle starts to write down Hugo's story.

Question: What broken thing are Hugo and his father trying to repair?
Answer: Automaton