To what extent is Hamlet's tragic fall a result of the morally corrupt world?How does his own free will influence his tragic fall?
Concerning Shakespeare's Hamlet, the issues of free will and a corrupt world are not necessarily connected.
Free will relates to fate or God's plan or, today, one's upbringing and genetics (nature vs. nurture) as deterministic. In Shakespeare's day, predestination was an issue, and the world was seen as ordered.
The issue of a corrupt world is not really related to the free will issue. Some see Hamlet as a moral and incorruptible human in a corrupt world. Just because he is a moral man surrounded by the corrupt, doesn't mean he doesn't have free will. He can be, let's say for argument sake, in a winless situation, but still have free will, his own choices to make. And he can have the power to make them. If I'm trapped in a situation that I can't win, I can still choose to go along or give in or commit suicide or kill someone else, or whatever. Being surrounded by corruption isn't the same as not having free will. The two are not necessarily connected.
And Hamlet certainly is surrounded by corruption. Ophelia, for instance, tries to play Hamlet just like almost everyone else in the play does. Hamlet doesn't reject her love, she uses his. She is a victim, too, of her father and her brother and of a patriarchal society, but she spies on Hamlet and returns his gifts in order to elicit a response. Hamlet doesn't reject her love. He rejects her thinking she is smarter than him and thinking that she can play him. You can argue that Hamlet overreacts, but you cannot argue that anyone but Ophelia initiates the destruction of their relationship. Horatio is the only character that comes to mind that doesn't try to trick Hamlet or pull something over on him, as they say.
Thus, viewing Hamlet as a moral man in a corrupt world is one option, or one way to interpret the play. You can argue that if Hamlet behaves morally, the tragedy is bound to happen. You can argue he cannot win, as a moral man in a corrupt world. But those arguments probably have nothing to do with the free will issue.
We all live in a morally corrupt world. I grant you, most of us don't have to deal with it on such a grand scale: a murdered father, a mother who remarried so hastily (to her brother-in-law, as well), or royal court politics. However, we all have things around us which are immoral and corrupt and which we can neither fix nor change. How we choose to deal with them is up to us.
Given that, Hamlet's fate is determined largely by his own free will. He did not have to seek revenge; he did not have to kill Polonious; he did not have to turn Ophelia's love away; he did not have to condemn Rosencrantz and Guildenstern to death; he did not have to act crazy and confuse those around him...and the list goes on. In short, while he has been burdened with a series of awful circumstances, he is a free agent who made those choices and must therefore live with the consequences.
That sounds pretty heartless, I know; and it's true Hamlet's problems are on a grander scale than most. So, while I claim his fate is the consequence of his free will, I also believe it is a tragic fall in the sense that his punishment may be more than he deserves. He was a victim of both his circumstances and his choices.
There seems to be two different questions emerging here. The first one assesses how the world is to have played a role in Hamlet's downfall. The answer to this would lie in the death of Hamlet's father and the usurping of his throne and wife. This unholy act is one that causes a great deal of pain in Hamlet, forcing him to question nearly everything around him. At the same time, the endless scheming that seems to be surrounding him with Claudius and others causes him to doubt nearly everything. This questioning and doubt plays an intense role in Hamlet's perception of reality and within his consciousness. At the same time, I would say that his own free will did play a role in how things resulted. There was a point where Hamlet was presented a way in which the world could have made sense. The love and character of Ophelia was one where there had been a great deal of sacrifice and sincere authenticity present. Hamlet's cruelty and sense of scorn with which he treated her is an example of how his own free will did play a role in his own condition. In the end, a brutal convergence of social conditions and individual weakness helped to doom Hamlet.