How does King Hamlet's death affect Hamlet as a character and his actions? How does this affect his relationships and behavior?

King Hamlet's death, especially after he appears to Hamlet as a ghost and tells him he was murdered by Claudius, weighs heavily on Hamlet, leading him into a spiral of depression in which he contemplates suicide. As Hamlet puts it

O, that this too too sullied flesh would melt,Thaw and resolve itself into a dew,Or that the Everlasting had not fix'dHis canon 'gainst self-slaughter!  

Much has been written about why Hamlet...

King Hamlet's death, especially after he appears to Hamlet as a ghost and tells him he was murdered by Claudius, weighs heavily on Hamlet, leading him into a spiral of depression in which he contemplates suicide. As Hamlet puts it

O, that this too too sullied flesh would melt,
Thaw and resolve itself into a dew,
Or that the Everlasting had not fix'd
His canon 'gainst self-slaughter!  

Much has been written about why Hamlet is so depressed: is it because, in the Freudian/Oedipal reading, he is gripped with guilt that he unconsciously wanted to do just what Claudius has done: kill his father and marry his mother? Or is his grief over his father's death simply magnified into depression because of his inability to act? Or is he, as Rene Girard contends, caught between an honor code that insists on revenge killing and a Christian code of forgiveness? 

Whatever the reason, throughout the play, Hamlet behaves erratically and expresses his anguish in soliloquies, displaying his groping for answers and understanding. His depression and the questions it raises about the meaning of life in a corrupt world affect his relationships as he pushes away Ophelia, whom he loves, and becomes alienated from his mother, his uncle and most of the courtiers that surround him. His behavior becomes so erratic that it calls into question his sanity.