So I was the one who started this thread, been a while since I've read it.
Some of the quotes from TDK Joker that, IMHO, reveal something about the Joker's personality, if not his (possible) background:
"I believe whatever doesn't kill you simply makes you stranger!" (Right away we can tell that the Joker's scars betray experiences that have made him who he is.)
"And I thought my jokes were bad!" (Here the Joker is playing on his own name, since he is supposedly a "funny clown", yet his "jokes" are sadistic and horrific.)
"If you're good at something never do it for free!" (The original script for this began with "As my mother used to say..." So the Joker clearly had a rough childhood, with his mother very likely being a prostitute.)
"No, I'm not...No, I'm No-tuh!" (crazy, obviously! The Joker thinks EVERYONE ELSE are the crazy ones, and HE is the sane one!)
"You want to know how I got these scars? My father...was a drinker, and a fiend!" (If he doesn't hate his father, he certainly doesn't think much of him by saying that he was responsible for why he who he is. Plus, telling a drug lord that his father was a "drinker and fiend" is telling, because it shows that the Joker will make every "origin" story personal to the person he's telling it to.)
"Look at me...LOOK! AT! ME!!!!"
Saying "You remind me of my father...I HATED my father!" to Senator Leahy (This is interesting, because Leahy is a man of authority. Perhaps the Joker's father was a man of authority? And perhaps he was a total two-faced hypocrite, who in public was a righteous man of authority, but in private, was abusive, even murderous, "a drinker, and a fiend."
The whole "So I had a wife" story he gives to Rachel...(again, making the story personal to the person he's telling it to. Also, the "Now I'm always smiling" line shows that the Joker sees humor and irony in the horror and chaos of life in general).
The interrogation scene (where he reveals to Batman his "rationale" for what he does)...MANY interesting and revealing quotes from this scene, including the following
"See, their morals, their code...it's a bad joke, dropped at the first sign of trouble! They're only as good as the world allows them to be, I'll show ya!" (the "bad jokes" of society at large make people act in what the Joker sees as stupid and hypocritical ways. He's "ahead of the curve" because he is, in his mind, the ultimate and inevitable product of "civilized society.")
"The only sensible way to live in this world is without rules, and tonight you're gonna break your one rule!" (This plays into the "Agent of Chaos", as the Joker later says, the anarchy and seeming randomness of pure chaos.)
"Don't worry, I'm going to tell you where they are...both of them! And that's the point, you'll have to choose!" (We can't escape death. In the Joker's view, we can only choose who we want to save, but in doing that, we cannot save everybody.)
The scene where he tells Gordon's man, "In their last moments, people show you who they really are..So, in a way, I knew your friends better than you ever did!" (The Joker believes that one's response to death reveals one's true self, and those who fear death have something to lose).
"It's not about money, it's about sending a message. Everything burns." (The Joker obviously doesn't care one iota about money, the material things in life. It's the psychological aspect of making people "choose" when faced with chaos that the Joker really relishes.)
The hospital scene with Dent, where the Joker talks about "schemers" and him being an "Agent of Chaos" (Here, the Joker shows that chaos reveals the fear that humans have of death, and the Joker, as he points the gun to his head, reveal that he is NOT afraid of death. This reveals that the Joker has the advantage over others, because he won't let his own death, which he is always coming close to, slow him down in his OWN "schemes." So the Joker may be a "schemer" too, but on a much, much more advanced level than the other schemers.)
The ferry scene, where the Joker again makes people choose between death and death (there's no escaping chaos, there's no escaping death, it's just a matter of whether or not you embrace the chaos).
And in the final Joker scene, where the Joker laughs as he falls to his death (but Batman saves him), the "unstoppable force meets an immovable object" line shows that the Joker can corrupt everyone to death, fear, chaos...everyone, that is, except Batman. So this is why he actually has some respect for Batman, because he is the purest opposite of who the Joker is. He is immovable and incorruptible, he doesn't budge even when faced with the most agonizing choices, with the most chaotic world...he is still Batman. So in that sense, he is the only one who could possibly defeat the Agent of Chaos that is the Joker.
So overall, the Joker's personal background is not as important as what he REPRESENTS...pure chaos, a relativistic and warped sense of morality, and his goal of converting everyone else to his way of thinking, of embracing the anarchy.