Is he mad or sane? Or just mad in craft, yet punished with sore distractions. Perhaps Hamlet is the victim--as we all at some time feel to be--of the world's sane view of insane perplexities. He is the man at war within himself; a traveler with a passport into strange, twilight regions of the soul.
Whether or not Hamlet's suffering, and then insanity, is caused by his relations or by his own melancholy, Hamlet's struggle embodies the essential inwardness of human suffering that all can relate to.
The concrete manifestations of Hamlet's misery are closely related. Not only has his father died, also his uncle is the murderer, his mother marries the uncle and is a likely accessory to the crime, and his true love lies to him. It is reasonable to suppose that Hamlet's state of mind becomes more and more unstable as he is consumed with thoughts of all of the sins against him. Eventually Hamlet loses all sense of life's significance.
He states to his deceitful mother and uncle, "But I have that within which passes show These but the trappings and the suit of woe" (I, II, 85-86). Hamlet tries to articulate that his grief for his father's death and the prospect of his mother's unfaithfulness is almost inexpressible. He is left alone to bear the burden of suspicion toward the people he once loved. To a man bereft of a sense of purpose there is no possibility of action because it wouldn't have any meaning. No act but suicide seems rational.
Yet Hamlet seeks to escape his life of woe when he is commanded by his father's spirit to a great act--revenge. Therein lies the unique chance for a sick soul to heal, to be cleansed and rested. But good cannot come of evil, and so the sickness of his soul only further infects his state of being. His mental disintegration, once proposed to be on purpose, continues uncontrolled.
In the desert of his mind, void with the utter emptiness of the knowledge of death (his father's and the death of his faith in his mother) lies the supreme enemy to neurotic despair: romantic love. For romantic love assures power, it can create a sense of purpose, inspire heroism and beauty. A lonely flower can overspread the desert with a multiplicity of color and fragrance. But since Ophelia has lied, Hamlet will not accept her into the only relationship that could save him from the trap; salvage his sanity. He is left alone to walk deeper into melancholy; a sickness of his mind or of his soul.
We properly know Hamlet himself only when he is alone with death because wherein death, not life, holds the deeper assurance for humanity.