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No.
Laurence Olivier starred in the 1948 version of Hamlet.
Yes, Mel Gibson did appear in the remake of Hamlet, released in 1990.He played the role of Hamlet.
Hamlet - 1995 was released on:
USA: 1995 (West Hollywood Independent Film Festival)
Hamlet. There are more than twice as many adaptations of Hamlet than of any other single Shakespeare play.