In Shakespeare's Hamlet, the character most isolated is Hamlet. He does not know whom he can trust, especially since his mother has remarried hastily after her husband's death, and Hamlet has discovered that his father may have been murdered by his uncle.
The only person Hamlet can confide in is Horatio, who is not part of the inner royal circle. There is no way for Hamlet to understand what is happening regarding his mother, uncle (Claudius), Polonius and Ophelia, other than by conjecture.
Hamlet cannot speak to his mother; he is not certain whether or not she played any part in Old Hamlet's death. He is also disgusted with her for her hasty remarriage, and for marrying her brother-in-law, which Elizabethans considered incestuous.
Polonius is a foolish man who will do anything to improve his image with, and service to, the King. Claudius, of course, disgusts Hamlet even before Old Hamlet's ghost speaks to him about his murder. He feels that Claudius is too loud, drinks too much, and will give the Danes a bad reputation because of his behavior. Hamlet is also unhappy because his mother has married Claudius.
Ophelia is the most distressing disconnect that Hamlet has to deal with because it would seem he truly loved her. However, she must follow the directions of her father and the King—she's a woman—and so she ends up spying for them. She has no choice, but Hamlet censors her strongly, rejects her and insults her.
I do not believe that Claudius and Polonius contribute to the isolation that Hamlet feels from the rest of the court, but his loss of connection with Gertrude and Ophelia would certainly cause an increased sense of isolation—beyond the loss of Hamlet's father.
Ophelia is isolated in that she really has no one to talk to. Hamlet has rejected her, and her brother and father are not supportive of Hamlet's place in her life. Gertrude is somewhat isolated as well. She is married to Claudius, but this marriage may well have been one of convenience. It guarantees that she will continue to live the life she is accustomed to, and that Hamlet will still have a connection to the throne.
The biggest problem with isolation in this play is that communication breaks down. Had Hamlet still been able to speak candidly with his mother and Ophelia, they might have been able to provide him with confidence, or information about what Claudius and Polonius were up to. It is only through Hamlet's isolation from the others that the tragedy can be played out.