According to the Declaration, the king denied life, liberty and happiness by preventing the colonists from establishing their own laws, making them in a way "prisoners" to the laws dictated across the sea which shouldn't have to apply to their life in the new continent.
Also by prohibiting them from trading with the rest of the world, the lives of colonists in America became dulled with the inability to reach out and expand their vision.
And finally by keeping armies in the new world during peaceful times and forbidding the new citizens to receive trial by jury.
By blocking their ability to pass laws, the king limited the colonists' liberty. By punishing and killing those who disagreed with him, he violated their unalienable rights.
The North and the South had pretty equal army sizes during the war. The North had a big industrial industry during this time. The Confederacy had 1/9 of industrial capacity compared to the North at the start of the war.
