During and immediately following Hamlet's conversation with the Ghost, he is determined to fulfill the Ghost's wishes. Hamlet already has a plan to catch Claudius. However, the next time he appears in the play, which is long after the Ghost's visit, he has not yet done the deed. He admits he may have been deceived by the ghost. "The spirit that I have seen / May be a devil, and the devil hath power / T' assume a pleasing shape (2.2.627-629).
To fully understand Hamlet’s inaction, it is important to look at revenge. In Richard III revenge is not exacted until Richard is dead and his fowl deeds found out. In Othello, Iago will not be revenged until Othello is completely destroyed. In Merchant of Venice Shylock wants to humiliate and then kill Antonio. Thus revenge is not exacted until the evil deeds of the offender are revealed and the public knows the truth. Only then does the thought of death come into revenge. Under this light, Hamlet cannot kill Claudius until he can prove that he poisoned the late king. Thus the first two acts are not only for the reader to understand Hamlet, but to allow Hamlet to gather needed evidence against his uncle.
It is not until act three, when Hamlet has not been able to prove his uncle is a murder that he decides to force Claudius’ hand. Hamlet comes up with the idea of the play to prove whether or not Claudius is guilty. But the play also causes another problem. Hamlet discovers Claudius’ guilt but has no evidence to present to the people. Thus, when Hamlet sees Claudius praying he stays his hand until he can absolutely prove his guilt. Another reason why Hamlet stays his hand is because Claudius is praying. It is Hamlet’s fervent belief that if he kills Claudius while he is praying he might go to heaven. Which makes the final lines of that scene so ironic. After Hamlet has left, Claudius says, “My words fly up, my thoughts,/ remain below:/ Words without thoughts never to heaven go”(lines 97-99). Claudius does not think that his words are reaching God. Thus if Hamlet would have killed Claudius, he still would have gone to hell.