How did the Declaration of Independence change the nature of the American Revolution?
It did not change the nature of the revolution. It was an announcement to the world that we considered ourselves a sovereign nation.
Until July 4, 1776 we were, as far as the world was concerned, a part of the United Kingdom. From that day forward we were autonomous and at war with a foreign country. Until that day we had been in a civil war with our mother country. But the final two statements were entirely reliant upon the war's outcome. If we had lost, we would still have been a colony of Great Britain and would have had to endure punishment for having taken arms against the king.
The early portions of the Declaration go to great lengths to delineate the purported crimes of the king upon America. It was our justification for both the war and our separation. It additionally was meant for the French as Benjamin Franklin had been working hard to gain the support. He had failed that far.
France was not on good terms with England anyway and with America calling itself a nation unto itself, it gave France what it needed to send support.