After Claudius's reaction at the end of The Murder of Gonzago, the reader should have no doubt that Claudius is guilty of his brother's murder. Just in case the reader wants further proof, Claudius speaks a monologue on his own, saying, "O, my offense is rank, it smells to heaven." Then he uses exact wording by saying the following:
But, O, what form of prayer / Can serve my turn? "Forgive me my foul murder"? / That cannot be, since I am still possessed / Of those effects for which I did the murder, / My crown, mine own ambition, and my queen.
Claudius actually admits to the murder. This text goes further in that Claudius actually names his own sins when he says, "My crown, mine own ambition, and my queen." Claudius's brother (Hamlet's father) had the position of power: the kingship. Claudius demonstrates envy because he is willing to do anything to get into that position of power. Then there is the echo of the flaw of Macbeth (who, if you remember, had the tragic flaw of "vaulting ambition") when Claudius names his own ambition for that same power of kingship and, further, his willingness to commit murder in order to achieve it. If one has an "intense and selfish desire for something, especially wealth, power, or food" that person feels the exact definition of greed. Due to this intense selfish desire (and apart from the fact that his brother was already in possession of those desires: the kingship and the queen), Claudius is definitely guilty of greed. Finally, due to Claudius' additional desire for Gertrude (yet another of the "effects" of the murder), Claudius is also guilty of lust. Why are these sins of envy, greed, and lust important? They are three of what the Roman Catholic Church called "the seven deadly sins." At the time, people were taught that all sins stemmed from these seven as the "origin" of all sin. In a way, this shows that Claudius is in no way a moral and noble character. In fact, he is the villain of the play (if you disregard the dishonest ghost theory).