What propels Hamlet-the prince's proud wish to avenge his father's death and assert his rights? A tragic flaw in his character or something else?
I don't think you can purify Hamlet's motives into a single motive. I think Hamlet's actions are based on a complex mix of his desire to avenge his father's death, his anger at his mother and Claudius, his own ambition, all mixed with his desire for a life of peace and happiness. In Act 1, sc. 5, when Hamlet is first asked by the ghost of King Hamlet to avenge his death, Hamlet swears that he will. At this point, Hamlet is shocked and quickly agrees to what his father's ghost asks. Later, in Act 2, sc. 2, Hamlet rails against himself and his lack of action, but says that he needs to be sure the ghost was telling the truth. Obviously doubt has crept into Hamlet's thinking since Act 1, sc. 5, and Hamlet doesn't want to commit murder without being sure of Claudius's guilt. If Hamlet was simply driven by a desire to get the throne from Claudius, he wouldn't need to prove the ghost's veracity. Also, in this speech, Hamlet says, "...And can nothing -no, not for a king / Upon whose property and most dear life / A damned defeat was made." It is interesting to note that Hamlet puts "property" before "dear life". This suggests that Claudius's marriage to Gertrude is as heinous to Hamlet as is Claudius's murder of King Hamlet. In Hamlet's Act 3, sc. 1 soliloquy, Hamlet suggests that fear makes people makes people inactive. He says that if people could act without fear of repercussion, they'd be more likely to act. This suggests that Hamlet fears what will happen if he kills Claudius. Will he go to hell? Will other penalties fall on him? Hamlet yearns for a life in which he is free to study, read, and spend pleasant hours with those he loves. Throughout the play, Hamlet wrestles with his hesitancy and his lack of action in avenging his father's death. He thinks and overthinks about all his actions which suggests that he would rather have a peaceful life than a powerful one.
I agree with luannw, but I also wanted to add that Hamlet is highly influenced by his mother's attitude - her lightheartedness after her husband's death. Hamlet sees his father's memory offended by her after he finds out that his father has been murdered by Claudus. When Hamlet sees Ophelia's coldness toward him, he is also personally offended ( and begins developing a personal hatred for women in general. )