Did the character have some illness like dementia or was he just off his rocker.
That’s not really the point of the book. It’s not a book about diagnosing Don Quixote, since there was no real “mental health establishment” to comment on. The story was a parody of the classic romantic tales being written at the time in several languages. It was written to show just how poorly someone who acted like a stereotyped romantic knight would get along in the real world (the answer is “very”).
No one asks if Leslie Nielsen’s characters are insane, since they’re not designed to be reflections of actual people. The point is that they act bizarrely.
Not sure there can be a sensible answer, because he is fictional. His every word and action is made up in Cervantes’s head, centuries before the modern understanding of mental illness came into existence. Unlike Sheldon Cooper, who is written with, loosely speaking, an autism spectrum disorder like what used to be called Asperger’s syndrome in mind, that is not possible for DQ.
An analogy - prior to the invention of cameras, horses were painted by artists doing the best they could to capture in still motion the fleeting memory they could grasp of the leg movements. We now know they were pretty much hopelessly wrong. Your question is akin to asking “What is the name of the gait of this horse in some 17th C painting”, when the gait doesn’t exist. You could ask what was the painter aiming at, because horse gaits have been known for some time, but with DQ, the present fundamental concepts of mental illness classification did not exist, so Cervantes can’t have been aiming at, for example, schizophrenia. Culturally, primitive ideas of madness blended with the notion of the “holy fool” are probably as close as one can get.
ETA Don’t mean to disagree with Speaker, either. His answer is more accurate. I just tried to remain within the parameters of the question as well as I could.
Well actually, in the 17th century, and even much earlier, people had some pretty sophisticated concepts, theories and classifications of mental disorders. See, for instance, Burton’s The Anatomy of Melancholy (1621). Their ideas back then did not entirely accord with what we believe now (not that we really understand most mental disorders very well even today), but they did have some ideas.
Nevertheless, although it is not altogether true that there was no “mental health establishment” back then, I think Speaker for the Dead* is right to say that Cervantes was not really trying to give any sort of realistic (even according to the theories of times) portrait of mental illness in his book. All the same, he was probably influenced by the theories and categories that were then in use. If you want to learn about them, Burton’s classic might be a good place to start. It is not only about melancholy.
*Who ought to know if anyone does. 
Wrong with Don Quixote? There was nothign “wrong” with him; there was (and still is) something very wrong with a world where the Ideals of Chivalry are considered to be nothing more than the ravings of a madman or a source of farcical humor.
A search for Quijote diagnóstico (there is a lot more literature on this subject in Spanish than in English, unsurprisingly), yields among its first responses a book which diagnoses Don Alonso with paranoid melancholy and an article (summary in English) which bets on delusional disorder for Don Alonso and shared psychotic disorder for him plus sidekick.
Cervantes’ own diagnosis is that he went off his rocker, but there is nothing in the books to indicate a progressive, degenerative condition - dementias are progressive.
“From too much reading and not enough sleeping, his brain dried up, and thus lost he his ability to reason”. I’m sure there are better translations out there, but this one is mine.
Don Quixote was the 17th century equivalent of someone who’s read too many comic books, and thinks they can actually dress in a costume and go out and fight crime. Picture someone wearing spandex with a big “Q” on their chest. Quixoteman!
Since this is about a literary character, let’s move it to Cafe Society.
Colibri
General Questions Moderator
It was basically a tale of political satire; Cervantes was criticizing the social order in the Spain of his time. Instead of industrializing and building up the country, the Spanish nobility were like Don Quixote-endlessly seeking chivalric adventures.
And his criticisms were largely correct-Spain went into a long period of decline, after the death of Philip II.
I love this place.
As an aside, do people have recommendations for translations of the novel?
Don Qick-Ass?
The Quixtion! Johnny Quix!
This is what I cam in to say, but you said it so much better than I could. So, I will climb on Rocinante and ride away. Come Sancho!
This is my quest, to follow that star …
No matter how hopeless, no matter how far …
To fight for the right, without question or pause …
To be willing to march into Hell, for a Heavenly cause …
And I know if I’ll only be true, to this glorious quest,
That my heart will lie will lie peaceful and calm,
when I’m laid to my rest …
And the world will be better for this:
That one man, scorned and covered with scars,
Still strove, with his last ounce of courage,
To reach … the unreachable star …
Oh my, Dr F. You ninjaed me.
Golly, I do love that song.
I sang it on stage in front of thousands one night many years ago.
Weirdly, I didn’t read Don Quixote until later in my college career.
“To reach… the unreachable star”
I still get a thrill down my spine reading that.
The problem isn’t that he’s chivalrous, it’s that he can’t see anything for what it is and lives in a fantasy world. Being courtly is kind of the least of his problems. But I agree that trying to diagnose him with a specific illness misses the point. He loses his mind in fiction, that’s all.
I’m actually wiping away a tear
He suffers from Bovaryism, a textually transmitted disease.
Sorry, I can’t claim I made that one up; I stole it from Daniel Pennac’s “Comme un roman”.
It was way long, for starters.