The case in question is episode 51 of The Venture Bros.:
Everybody Comes to Hank’s
This is one half of a two-part story from season 4 with each half telling about the summer vacation of one of the titular Venture Brothers. It is like the Venture Brothers version of Tiny Toon Adventures: How I Spent My Vacation. Episode 51 starts with Dr. Venture demanding that Hank get a job over the summer which prompts Hank to starts a chain of small business including working as a private eye. Hank starts with the “case” of his friend Dermott’s mom not coming to pick him up after work. Dermott’s mother almost immediately picks him up but Hank starts working on the much more interesting case of who is Dermott’s unknown father. The gimmick of the episode is that whenever they are on the case everything has a black and white film noir aesthetic and the dialog is the straight out of a hard boiled detective novel.
While the Venture Brothers is not normally a detective cartoon they do like to take from all assets of popular culture for their stories including this dead on send up of the old hard living detective stories. Hank is of course dressed like a pulp fiction detective in the vein of Sam Spade or Philip Marlowe and has dialog to match. The Alchemist plays along out of boredom as Hank’s side kick and several other characters by accident or design look the part as well. Dermott’s sister Nikki fits perfectly into the role of the femme fatale with the characteristic flirting and steamy love scene included. There are also the prerequisite scenes where informants are questioned over narration, an uncooperative witness needs to be roughed up, and a classic chase sequence. It is both a well done parody and homage to many notable noir films and novels with Chinatown being the main target.
The mystery itself was one that had been debated by fans since season 3 when Dermott had first been introduced. Most people assumed that his father was Brock but of course the show never plays anything that simply. So when the big reveals comes it is always the last thing you would expect. The case is actually solved literally by magic so most the detective work that comes before it is all for naught but such it the way of a show whose main theme is failure. It was fun episode that stood out for many fans of the show (including me) for its style and humor making it a huge success.