How does the graveyard scene in Act 1, scene 5 of "Hamlet" contribute to the audience's understanding of Hamlet's character?

In "Hamlet," the appearance of the ghost of his father is most disturbing to Hamlet, of course. Yet, the king's spirit demands that Hamlet avenge his murder--"If thou hast nature in thee, bear it not" (I,v,81)--but  not punish the queen for marrying his murderer, his brother:

Taint not thy mind, nor let thy soul contrive/Against thy mother aught.  Leaver her to heaven,/ And to those thorns that in her bosom lodge/To prick and sting her (I,v,85-88)

This mixed order serves to create for Hamlet an anguish which halts his revenge against Claudius for four more acts and several more soliloquies.  Even at the end of Act I, Hamlet indicates his ambivalence:  For, as he bids goodby to Horatio and Marcellus, Hamlet writes in his memorandum book and says,

Now to my word...I have sworn't. (I,v,110-112)

But, when Hamlet bids adieu to the ghost, he reflects,

The time is out of joint.  O cursed spite/That ever I was born to set it right! (I,v,187-188)

indicating his reluctance to act.  The appearance of his father's ghost causes Hamlet to consider regicide which he hesitates to commit since he could be put to death himself for such an act.  Still, in Act II he berates himself that he cannot bring himself to commit the act of revenge for which he has more "motive and cue for passion" (II,ii,517) than the actor whom he watches, an actor who conveys more spirit than Hamlet.  In his soliloquy, Hamlet continues his self-recrimination:

Why, what an ass am I!  This is most brave,/That I, the son of a dear father murdered,/Prompted to my revenge by heaven and hell,/Must like a whore unpack my heart with words,/And fall a-cursing like a very drab,/II,ii,539-543)

That he cannot punish his mother is extremely frustrating to Hamlet as he is disgusted with the lust she displays at her age as well as her disloyalty to his father's memory:

Fraility, thy name is woman" (I,ii,146)...O shame, where is thy blush? (III,iv,82)

While his melancholy increases, so does Hamlet's inaction.  Having been prevented from acting against his mother tortures Hamlet mentally, and this anguish causes him to continue his deliberation rather than acting.  In fact, Hamlet even contemplates suicide in his famous "to be, or not to be" soliloquy.  But, "conscience does make cowards of us all"(III,i,83) as Hamlet worries about the spiritual punishment for suicide.

In Act III, Hamlet continues his self-debate:  He considers avenging his father's death as he sees Claudius alone; however, he realizes this killing would benefit Claudius:

A villain kills my father, and for that,/I his sole son, do this same villain send/To heaven. (III,iii,76-78)

Finally, Hamlet with his "dull revenge" (IV,iv,32) sees Fortinbras with his army and realizes that this prince is willing to die on a battlefield for the mere sake of honor, Hamlet is moved to action:

Witness this army of such mass and charge,/Led by a delicate and tender prince,/...Exposing what is mortal and unsure/To all that fortune, death, and danger dare,/Even for an eggshell.  Rightly to be great/Is not to stir without great argument,/But greatly to find quarrel in a straw/When honor's at the stake.  how stand I then,/That have a father killed, a mother stained,/Excitements of my reason and my blood,/And let all sleep, while to my shame I see/The imminent deth of twenty thousand men/That for a fantasy and trick of fame/Go to their graves like beds....O, from this time forth,/My thoughts be bloody, or be nothing worth!(IV,iv,47-66)

So, by the end of Act IV, Hamlet is where he started from in Act I.