What role did the political parties play in the election of 1796

None at all. Throughout the states, there was a general assumption that Washington would be the first president under the constitution. When the electoral college met in New York in February of 1789, George Washington was elected President. When Jefferson who represented the agrarian south and Hamilton who represented the commercial north, left Washington’s cabinet as political parties started to merge. The election of 1796 was the first major political contest between Republicans and Federalists. John Adams ran as a Federalist and Thomas Jefferson as a Republican.