Hamilton served his country in many ways: he fought in the American Revolution against the British; led the efforts to reform the inadequate Articles of Confederation; helped design the American government as outlined in the Constitution; and even secured its ratification by writing the Federalist Papers.
There are several ways in which being nonaligned would have offered an advantage and disadvantage to a developing nation during the Cold War, but in general they would have been able to trade with both sides.
The classical heritage of Rome, the customs of various Germanic tribes and the belief of the Roman Catholic Church were the three roots of medieval culture in Western Europe.