What rights did the colonist believe they were guaranteed and were being denied?

They considered themselves to be Englishmen.

Explanation:

Prior to the Declaration of Independence in 1776, the people of the 13 colonies considered themselves Englishmen first and Americans 2nd. For the 10 years preceding the war, they continuously pushed for a seat in parliament as was the right of all Englishmen. They were always denied. The properly argued, even if unsuccessfully, that it was their right as Englishmen dating back to the Magna Carta to be afforded that right.