Discuss the internal conflict/dilemma that Hamlet struggles with in this speech.
How all occasions do inform against me. And spur my dull revenge! What is a man, If his chief good and market of his time Be but to sleep and feed? A beast, no more. Sure he that made us with such large discourse. Looking before and after, gave us not That capability and god like reason to fust in us unus'd. now, where it be Bestial oblivion or some craven scruple Of thinking too precisely on the event, A thought, which, quarter'd hath but one part wisdom and ever three parts coward, 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. Examples gross as earth exhort me: Witness this army of such mass and charge led by a delicate and 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,even for an egg shell.Rightly to be great is not to stir without great argument,but greatly to find quarrel in a straw when honours at the stake.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, that, for a fantasy and trick of fame, go to their grave like beds, fight for a plot whereon the numbers cannot try the cause, which is not tomb enough and continent to hide the slain? O! from this time forth, My thoughts be bloody, or be nothing worth!
The speech you cite occurs in Act IV, Scene 4 of Hamlet.
Just before Hamlet speaks these words, he has been talking a captain from Fortinbras' army. He learns from him that Fortinbras and the army mean to fight over a worthless piece of land in Poland.
Upon hearing that, he starts to scold himself in the speech you're talking about. His internal conflict is whether he wants to avenge himself for his father's death and his mother's dishonor or not. He is unhappy with himself because, as he notes, the army is willing to spill blood over something worthless while he hasn't done anything to avenge his father's death and his mother's dishonor (something very important).
So, his internal conflict is that he really feels that he ought to do something to take revenge, but it's pretty much against his more reflective, philosophical nature to do so.