Boromir alluded to the problems in Gondor when he was talking with Aragorn in Lothlorien (in the movie) but I think that other matter pushed Denethor over the edge, surely exacerbated by Boromir's death.
BTW, one of my favorite parts in that Lothlorien scene is when Boromir asks Aragorn if he has ever been 'called home by the sound of silver trumpets'. That makes Aragorn's statement at Boromir's death in the extended version even more poignant. Paraphrased: "They will watch for him from the towers, but he will not return."