Aragorn served with Thengel of Rohan (father of Theoden) and Ecthelion Steward of Gondor (father of Denethor) from 2957 to 2980, at which time he went to Lothlorien. Denethor was born in 2930 and Aragorn in 2931, so they were contemporaries and pretty young at the time. Ecthelion, and in fact the people of Gondor, loved Thorongil, who functioned as a captain of Gondor.
[QUOTE=The Tale of Aragorn and Arwen, J.R.R.Tolkien]
There was dismay in the City at the departure of Thorongil, and to all men it seemed a great loss, unless it were to Denethor, the son of Ecthelion, a man now ripe for the Stewardship, to which after four years he succeeded on the death of his father.
Denethor II [that’s our Denethor] was a proud man, tall, valiant, and more kingly than any man that had appeared in Gondor for many lives of men; and he was wise also, and far-sighted, and learned in lore. Indeed he was as alike to Thorongil as to one of nearest kin, and yet was ever placed second to the stranger in the hearts of men and the esteem of his father. At the time many thought that Thorongil had departed before his rival became his master; though indeed Thorongil had never himself vied with Denethor, nor held himself higher than the servant of the father.
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In short, the real Denethor (as opposed to the PJ version) was as like to Aragorn as two peas in a pod, except that Denethor showed his age, and also that Aragorn had that certain something that allowed him to win friends and influence people (I’m guessing a lack of overt pride). But Aragron did not in any way base his claim on his earlier time in Mina Tirith as Thorongil. Perhaps if Denethor had opposed his claim, he might have mentioned it, but between the people of renown (Dol Amroth, Gandalf, the Elves) who already believed in Aragorn, his carrying Anduril (The Blade that was Broken), and his healing power*, I think Aragorn would have been accepted as king without reference to that time. But as I said earlier in the thread, I think Denethor’s pride would have led him to abdicate once he saw which way the wind was blowing. After all, he was the one who insisted that they were Stewards, not Kings to Boromir.
*Ioreth, an old woman, in the Houses of Healing (italics Tolkien’s):
For it is said in old lore: The hands of the king are the hands of a healer. And so the rightful king could ever be known.