A case can be made that Hamlet has relevance to the modern audience. The fundamental question that emerges from Hamlet is how does one address the issue of injustice in the world? Hamlet's father has been unjustly killed and those in the position of power do not merit it. This is where Hamlet engages in his intense questioning. It is also a condition that faces individuals in the modern setting. Injustice is present and there are individuals in the position of power who do not merit the position they hold. Hamlet's struggle to find justice and moral order in a world that does not display it is a significant theme that has relevance to the modern setting.
I think that another interesting condition of the drama that can be relevant in the modern setting is the idea of emotional cruelty. Hamlet has feelings for Ophelia. Yet, he submits her to the worst of abuses and the most intense of disrespect. The idea of personal cruelty is relevant to the modern setting. Hamlet's most vicious tendencies are displayed on someone who is probably the most tender in the drama. Essentially, one is left wondering how individuals could mistreat people for whom they have feelings? In the modern setting, this same question is posed whenever we see issues of domestic violence, child abuse, or other instances where some of the most savage of behaviors are displayed towards individuals who should not be the recipient of such torment. This is another way in which the play connects to the modern audience.