Why does hamlet didn't take revenge from his uncle, when he knew that he was the killer?

Ok so Hamelt delays killing Claudius for many reasons: (1) Considered against the background of ancient Greek and Roman revenge tragedies, the Ghost's command to "kill the king, but spare the queen" is like saying "make an omlette, but don't break any eggs." Hamlet has trouble working up just enough anger to punish murder, but tempering it with just enough compassion to spare (what was then regarded as) incest. (2) Hamlet delays killing others for the same reason he delays killing himself -- being poised on the edge of death (either inflicting it or suffering it) leads him to a series of highly illuminating moments and insights that Hamlet shares with us, particularly in the soliloquies, and he wants to extend this "self- educational" moment of crisis and see where it leads. (3) On a more mundane level, Hamlet wants to be completely convinced of Claudius's guilt first -- and as soon as he gets proof (The Mousetrap), Claudius virtually arrests Hamlet and whisks him out of the country. (4) It takes Hamlet a while to work up the nerve to commit regicide face to face and deliberately -- he tries in impulsively in act IV but kills the wrong man, Polonius; then proceeds to a more deliberate dispatch of Rosencrantz and Guildenstern...finally after having "practiced" in this way, he's ready to do the deed in Act V. I have submitted an extended essay on reasons 2 and 4 which I believe will soon be posted at www.hamlet.org.