In 1941, Barton Fink's first Broadway play, Bare Ruined Choirs, has achieved critical and popular success. His agent informs him that Capitol Pictures in Hollywood has offered him a thousand dollars per week to write film scripts. Barton hesitates, worried that moving to California would separate him from "the common man", his focus as a writer. He accepts the offer, however, and checks into the Hotel Earle, a large and unusually deserted building. His room is sparse and draped in subdued colors; its only decoration is a small painting of a woman on the beach, arm raised to block the sun.
In his first meeting with Capitol Pictures boss Jack Lipnick, Barton explains that he chose the Earle because he wants lodging that is (as Lipnick says) "less Hollywood". Lipnick promises that his only concern is Barton's writing ability and assigns his new employee to a wrestling film. Back in his room, however, Barton is unable to write. He is distracted by sounds coming from the room next door, and he phones the front desk to complain. His neighbor, Charlie Meadows, is the source of the noise and visits Barton to apologize, insisting on sharing some alcohol from a hip flask to make amends. As they talk, Barton proclaims his affection for "the common man", and Charlie describes his life as an insurance salesman. Later, Barton falls asleep, but is awakened by the incessant whine of a mosquito.
Still unable to proceed beyond the first lines of his script, Barton consults producer Ben Geisler for advice. Irritated, the frenetic Geisler takes him to lunch and orders him to consult another writer for assistance. While in the men's room, Barton meets the novelist William Preston (W.P.) "Bill" Mayhew, who is vomiting in the next stall. They briefly discuss movie writing and arrange a second meeting later in the day. When Barton arrives, Mayhew is drunk and yelling wildly. His secretary, Audrey Taylor, reschedules the meeting and confesses to Barton that she and Mayhew are in love. When they finally meet for lunch, Mayhew, Audrey, and Barton discuss writing and drinking. Before long, Mayhew argues with Audrey, slaps her, and wanders off, drunk. Rejecting Barton's offer of consolation, Audrey explains that she feels sorry for Mayhew since he is married to another woman who is "disturbed".
With one day left before his meeting with Lipnick to discuss the movie, Barton phones Audrey and begs her for assistance. She visits him at the Earle, and after she admits that she wrote most of Mayhew's scripts, they apparently have sex; Barton later confesses to Charlie they did so. When Barton awakens the next morning, he, again, hears the sound of the mosquito, finds it on Audrey's back, and slaps it dead. When Audrey does not respond, Barton turns her onto her side only to find that she has been violently murdered. He has no memory of the night's events. Horrified, he summons Charlie and asks for help. Charlie is repulsed but disposes of the body and orders Barton to avoid contacting the police. After a meeting with an unusually supportive Lipnick, Barton tries writing again and is interrupted by Charlie, who announces he is going to New York for several days. Charlie leaves a package with Barton and asks him to watch it.
Soon afterward, Barton is visited by two police detectives, who inform him that Charlie's real name is Karl "Madman" Mundt. Mundt is a serial killer wanted for several murders; after shooting his victims, they explain, he decapitates them and keeps the heads. Stunned, Barton returns to his room and examines the box. Placing it on his desk without opening it, he begins writing and produces the entire script in one sitting. After a night of celebratory dancing, Barton returns to find the detectives in his room, who, after handcuffing Barton to the bed, then reveal they've found evidence of Mundt's latest murders. Each of the men notes how hot it is, and Charlie appears, and does the same; soon the source of heat is revealed: the hotel has become engulfed in flames. Running through the hallway, screaming, Charlie shoots the policemen with a shotgun. As the hallway burns, Charlie speaks with Barton about their lives and the hotel, breaks the bed frame to which Barton is handcuffed (thus freeing him), then retires to his own room, saying as he goes that he paid a visit to Barton's parents and uncle in New York. Barton leaves the (still-burning) hotel, carrying the box and his script. Shortly thereafter he attempts to telephone his family, but there is no answer.
In a final meeting, a disappointed Lipnick, in uniform (as he attempts to secure an Army Reserve commission), angrily chastises Barton for writing "a fruity movie about suffering" then informs him that he is to remain in Los Angeles; although Barton will remain under contract, Capitol Pictures will not produce anything he writes so he can be ridiculed as a loser around the studio while Lipnick is in the war. Dazed, Barton wanders onto a beach, still carrying the package. He meets a woman who looks just like the one in the picture on his wall at the Earle, and she asks about the box. He tells her he does not know what it contains nor who owns it. She then assumes the pose from the picture.

Question: What is Barton doing when he discovers Audrey's death?
Answer: swatting a mosquito
Alternative answer: Killing a mosquito