The character of Hamlet stands quite by itself. It is not a character marked by strength of will or even of passion, but by refinement of thought and sentiment. Hamlet is as little of the hero as a man can well be : but he is a young and princely novice, full of high enthusiasm and quick sensibility - the sport of circumstances, questioning with fortune and refining on his own feelings, and forced from the natural bias of his disposition by the strangeness of his situation...Still he does nothing; and this very speculation on his own infirmity only affords him another occasion for indulging it. It is not from any want of attachment to his father or of abhorrence of his murder that Hamlet is thus dilatory; but it is more to his taste to indulge his imagination in reflecting upon the enormity of the crime and refining on his schemes of vengeance, than to put them into immediate practice. His ruling passion is to think, not to act: and any vague pretext that flatters this propensity instantly diverts him from his previous purposes.The question is not so much, Why did Hamlet delay killing Claudius? The question is, Why did Hamlet feel obliged to do as his father's ghost commanded him? Honour, revenge, retribution - all these apply, but I feel it is not enough to compel a man of refined and exalted sensibilities to murder his incestuous uncle. He himself thinks murder is barbaric, the way he thinks the celebrations of the royal succession barbaric, full of drink and song. These ancient customs were present in his father's reign, and we know Hamlet senior was a conqueror of lands, brave and mighty, most unlike his more intellectual and quiet son. I fancy him as a hearty, masculine, less refined and more brash man. This was at odds with Gertrude, who preferred Claudius' way with words. Claudius' skills are more modern: he is smooth of tongue, whereas his brother is warlike, which attracted Gertrude. Like Claudius, Hamlet is a modernist - a thinker rather than a conqueror. Claudius is a diplomat, not a fighter (though arguably he is a corporate killer when he murdered his brother). King Hamlet's character is not portrayed in the script, but it is important that we infer it from the stereotypes implied by Shakespeare - universal stereotypes that are often true.
And yet Hamlet doesn't seem to resent his father: he practically hero-worships the man. He compares King Hamlet to a Hyperion, Claudius to a satyr (even before he knew Claudius murdered his father), which shows you his distaste for Claudius is not wholly due to the murder or incest, but because Claudius is nothing compared to King Hamlet. Hamlet is more refined and disliked the Vikinglike customs his father would have upheld (conquering and drinking and noise-making) so why all this reverence? King Hamlet was a strong-minded conqueror, a true man so to speak - something Hamlet could never be. Hamlet admires the strong brashness of Fortinbras, who can be unwise (less thoughtful than our Danish prince), an admiration whose validity we should question. Fortinbras sacrifices his soldiers to fight for a useless plot of land for sheer honour. Hamlet is more thoughtful and educated, and he ought to be proud of this. Yet he is not. He knows he is not what his ideal of a king ought to be - he is not feudal and majestic, he is a gentle democrat. His best friend is not a lord but an ordinary student, Horatio.
Then remember Claudius may have married Gertrude for strong government reasons - it is more convenient for him to marry the widow of the dead ruler, so he gets the power instead of the young immature Hamlet. Hamlet would have been expected to marry a royal - perhaps Fortinbras' sister (assuming he had a sister). But he loves Ophelia. This is why Polonius tells Ophelia not to be too close to Hamlet, because Hamlet will not be able to marry a commoner (though the daughter of an important Councillor). If King Hamlet were alive he might have prevented Hamlet from marrying Ophelia. Hamlet ought to resent his father. But he does not. The King would have been justified in getting his son married to a powerful lady to strengthen Denmark's power. Hamlet knows this, and King Hamlet's expectations of his son would have been against young Hamlet's nature. Young Hamlet feels insignificant because he is not naturally inclined to those qualities which made his father a ruthless ruler. Thus his love for Ophelia is a weakness. As Hazlitt says, he neglects her at first not because he stops loving her, but he is distracted by moral thoughts he could not confide in the immature less intelligent girl. Ophelia would have been in her teens and sheltered - not his intellectual equal. The late king may well have pressured his son to be more like him.
Hamlet's resolve to kill his uncle, therefore, is to prove he can be as good as his father. The murder, he feels, will prove his manhood and ability to be ruthless and decisive. But it is against his morals and inclination, much as he hates Claudius. No one, he says, could be his father, and that applies to himself. With a weak king on the throne, Hamlet must prove to himself that he is better than Claudius, the new king. As Hamlet is a young man, this eagerness to prove he can be good is only to be expected. The script says he is thirty but his thoughts imply a young man of twenty. The actor playing Hamlet, Richard Burbage, was in his thirties, so probably that was why Shakespeare said thirty. But a thirty-year-old man could not be Hamlet. Hamlet's feelings of inadequacy stem from the stern rule of his father, not so much the fact Claudius stole his rightful position as king. He would rather think than govern. He grieves unduly for his father not because he loved the old man, but because he knows he could never rule the place as well as the late king, and so feels inadequate. He is not ready to rule and feels lost. Instead of studying as he wishes, he must learn the ropes of ruling from Claudius. And with Claudius usurping the throne he has no chance to prove himself as king. Also, the old king must have allowed him to study, giving him a chance to prove himself intellectually (if not majestically). Claudius did not, cutting Hamlet from his source of pride and pleasure - his intellect. At the same time Hamlet knows an intellectual cannot do as much as a conquering king can (this was before the Renaissance after all) and wouldn't be acknowledged as great or powerful. Think of the struggling scholar as opposed to the industrialist.
The final ruthlessness in Hamlet is to prove his ability to be a conqueror but he fails as Shakespeare intended. Forget the Oedipal complex theory. As Hazlitt said, Hamlet cannot be acted on stage by an actor: he is a gentleman and a scholar, and wears and air of pensive melancholy.