Where in the play does Hamlet recognize his own failures to be the man needed to avenge his father's death?
Hamlet is unsure of himself throughout the play, but is especially aware of what he perceives as his own shortcomings in Act IV, Scene 4, when he witnesses the army of young Fortinbras, who is about his age, passing through Denmark on the way to attack the Poles. Marveling at the courage of Fortinbras and his men (as well as their opponents) who are about to risk their lives over a conflict where nothing but honor is at stake, he chastises himself, asking:
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, while to my shame I see the imminent death of twenty thousand men...
Hamlet, shamed, resolves to focus on avenging his father's death:
O, from this time forth,
My thoughts be bloody, or be nothing worth!
Though Hamlet seems to have gained some clarity of purpose, it is still only his duel with Laertes, and the knowledge that his wound from the duel is fatal, that spurs Hamlet to avenge his father's death through the killing of Claudius.