"The War Game," "Testament," or "Threads."
Two uber depressing nuclear war movies of fictional content. One features complete hopelessness and despair, British style; the other features complete hopelessness and despair, San Francisco Treat style. Both are well written, well acted, well directed films, classics of their genre. Neither have the slightest spark of humor or hope in them in the slightest, the British one, "Threads" being generally described as a Movie that makes "The Day After" (the movie that made Ronald Reagan negotiate a nuclear arms treaty) as a jolly romp in the park.
For extra points, how about the Academy Award Winning "The War Game" (won the 1965 for best documentary). So depressing the BBC would not show it for 20 years, although the actual gore in it is NOT extreme by 21st Century standards.
Make these funny, eh? The ULTIMATE Comedic Challenge. Are you MEN enough?
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Thomas Mossman commented
You can't make Threads funny without going full-on sociopathic.