It is difficult and quite possibly fruitless to compare and seek to connect such disparate works of literature as these three are.
Fifth Business is about a young man (first as a boy) who tries to find his way through life after an unfortunate accident gave him a guilty relationship with a woman whose life was altered because of a rock-loaded snowball meant for him.
Hamlet is about a young man who seeks to define his role and selfhood in a conflicting situation after receiving a command to seek revenge from his dead father and King.
J. Alfred Prufrock is about a young man who is lamenting his ineptitude romance for a woman he loves from afar.
One might say, if one needed to find a connection between the three dissimilar works, that the connection is that in each a young man is struggling to find his identity in difficult circumstances.
Fifth Business: I felt myself tied to her by the certainty that I was responsible for her straying wits, the disorder of her marriage, and the frail body of the child who was her great delight in life.
I do not know
Why yet I live to say 'This thing's to do;'
Sith I have cause and will and strength and means
To do't. Examples gross as earth exhort me:
... How stand I then,
That have a father kill'd, a mother stain'd,
Excitements of my reason and my blood,
And let all sleep? (IV, iv)
J. Alfred Prufrock: And indeed there will be time
To wonder, "Do I dare?" and, "Do I dare?"
Time to turn back and descend the stair,
It is impossible to say just what I mean!