How is Hamlet melancholic?

Scholars who believe that melancholy is Hamlet’s tragic flaw believe that Hamlet “thinks too much” and this “thinking too much” makes Hamlet excessively sad and thoughtful. Ornstein is famous for naming this particular tragic flaw. Just as the long soliloquy that is considered Hamlet’s “to be or not to be” speech can be considered evidence of inaction, it can also be submitted as evidence of melancholy. Shakespeare loved soliloquies. They are found in every single one of his plays. Many scholars consider Hamlet’s “to be or not to be” speech as the most important, existential, and metaphysical soliloquy of all time. It is here that Hamlet weighs the major advantages and disadvantages of being alive. Many scholars conclude that Hamlet is contemplating suicide. (I must include here, though, that there are scholars who disagree and think Hamlet is simply contemplating his own lack of action through thought, which may also lend to Hamlet’s tragic flaw of melancholy.) The entire soliloquy is Hamlet giving his reasoning (to himself and the audience) for contemplating that suicide. Hamlet makes the case that this world is full of sorrow and pain. Hamlet further muses that this suicide is actually “devoutly to be wished," but Hamlet stops his suicide because of his fear of the afterlife. If Hamlet considers death “sleep,” then he is worried about what happens in the “dream” for the soul who kills itself. A bit of background on Hamlet’s melancholy here is that the Roman Catholic Church teaches that the sin of taking one’s own life is one of the most serious sins and cannot be forgiven, leading the soul directly to hell (except in the case of desperate, immediate, and final forgiveness in the moments before death). A full forty lines of soliloquy are devoted to Hamlet contemplating this grim idea. Can you think of a more melancholic subject? The scholars who believe this soliloquy has been misplaced and that it isn’t about suicide at all but rather about “troubles of turning thought into action” also give a perfect explanation for the tragic flaw of melancholy.
Let’s look at some more specifics from the speech to point to more melancholy. In lines 85-89, “Thus the native hue of resolution / Is sicklied o'er with the pale cast of thought, / And enterprises of great pitch and moment, / With this regard their currents turn awry, / And lose the name of action." How is this melancholy? Well, Hamlet is convinced that “the native hue of resolution” is being “sicklied ‘o’er with the pale cast of thought.” Some point to the idea that here Hamlet names his flaw when he says “the pale cast of thought.” That is melancholy. Of course, you add the “lose the name of action” idea and you have fodder for the flaw of inaction. Therefore, this quote can be used to prove either flaw. Even if you lean toward the inaction flaw here, you can’t deny that the reason behind his inaction is contemplation of suicide or sad musings on the afterlife or thoughts about esoteric wisdom or the random gyrations of the mind.
Leaving the contemplation of suicide and looking at Act IV, Scene 4 because here is yet another soliloquy that provides ample evidence for the flaw of melancholy. All one needs to do is look at the precise first lines: "How all occasions do inform against me / and spur my dull revenge!" Although this line can be used (to a lesser extent) to prove the flaw of inaction, what is important here is that what Hamlet is constantly doing is precisely “thinking” about acting, while not actually doing so. Now we have Hamlet again naming his flaw, or at least his condition: "A thought which, quarter'd, has but one part wisdom / And ever three parts coward." In other words, Hamlet’s thoughts are mostly cowardice, and only one quarter intelligence.
Here are some more of Hamlet’s words to consider in regards to melancholy: "I do not know / Why yet I live to say 'This thing's to do,' / Sith I have cause, and will, and strength, and means / To do't." It is a wonder that Hamlet can repeat the exact same thing again and again. Hamlet is revealing (again) how he has the motive to do what he needs to do (avenge his dad). How melancholic. Yet again, saying the same thing in different words: The "tender prince, / Whose spirit with divine ambition puff'd, / Makes mouths at the invisible event, Exposing what is mortal and unsure / To all that fortune, death , and danger dare." Now Hamlet is talking about actually having “divine ambition” to do what he needs to do even though it is dangerous. He is standing and talking: idle again.
Let’s look at yet another: "Rightly to be great / Is not to stir without great argument, / But greatly to find quarrel in a straw / When honour's at the stake." Here it is honor that is at stake, but again it is Hamlet simply talking about that honor and not acting on it. This particular quote requires a bit more explanation. If “honour’s at the stake” and your dad has his life taken by your uncle, it would be important for the son to kill that uncle out of honor. “Stir” without any delay, and not finding “quarrel in a straw” (even if it’s one of his father’s lands) so that there isn’t anything getting in the way of what needs to be done. As a reader, you will notice that a support is better used for the flaw of melancholy (as opposed to inaction) if Hamlet doesn’t really have an opportunity to act at that moment (such as when Claudius is praying).
How about this example: "How stand I then, / That have a father kill'd, a mother stain'd, / Excitements of my reason and my blood, / And let all sleep." Hamlet is basically saying, “Here I stand, again not acting, even though my mom is sinful and my uncle killed my dad and, yet, I let it all go (or ‘sleep’) by not acting.” Another moment when Hamlet doesn’t really have an opportunity to act, but stands deep in thought is in Act IV when he says, after another grand soliloquy, “O, from this time forth, / My thoughts be bloody, or be nothing worth!” This line is particularly interesting because Hamlet talks about how important it has been, even before this, to get on the ball and avenge his dad, and yet he still stood around talking. In fact, he continues to stand around talking now. Does Hamlet need to clear his conscience yet again before acting? Interesting that he says only his “thoughts” will be bloody. That makes me laugh, actually. Has he been listening to himself talking? His whole point is that honor requires more than just bloody “thoughts.” It requires action.
As a final thought, I would like to assert that almost any of Hamlet’s soliloquies could be use to show the tragic flaw of melancholy. Hamlet is always thinking and talking to himself about those (often sad) thoughts. Therefore, as a researcher of this topic, any soliloquy could be used as support for melancholy as the tragic flaw.