This is shown by his lamentation that the everlasting had fixed his cannon against self-slaughter, thus preventing Hamlet from committing suicide at a time when he felt like doing so. If Hamlet were to kill Claudius, he would be violating a central religious principle against murdering another human being. This would make him feel guilt at having violated religious coda, thus representing estrangement at the level of his religious consciousness. .
Moral estrangement: Hamlet is also principled in a moral, or more generally a normative, sense. To kill a king would mean violating his internal conviction against committing crimes that might harm the hierarchical order of a state's government. His generally principled nature is shown by his refusal to gather together a mob to oust Claudius, as Laertes attempts to do later in the play, even though he knew that he had the ability to do so. The fact that he knew this is shown by the fact that Claudius explicitly knew this of Hamlet. One may safely assume that Hamlet's understanding of how politics works is virtually identical to that of Claudius and Hamlet Sr. The general similarity in how these blood relatives think and feel emerges from both of them professing their psychological reliance on Gertrude's support of them. .
Estrangement from countrymen: It is true that Hamlet has both the capacity to organize a mob of supporters to overthrow Claudius and is loved by most of his countrymen (to the point where, as Claudius admits, Claudius cannot openly think, feel or act in a hostile manner towards Hamlet). However, Hamlet is unable to organize such a mob for this purpose due to his principled nature, which prohibits him from doing so. Without this option, the only way for him to avenge his father's death is by himself alone taking action against Claudius. Essentially, then, he is one man up against a king and his army of soldiers, spies and friends.