In Othello, is Iago's account of being passed over for promotion the main cause of his hatred of Othello? Is the account he gives...

You must be careful, when reading a play, not to be too
quick to look for "certain" proof of a character's motivation.  You can certainly find
all the evidence you might need for confirmation of things a character says, but, since
all the reader of a script is given is what that character says (not the most reliable
source of accuracy) and what other characters say about him/her (an even more unreliable
source of accuracy), a reader is destined never to know for sure what motivates a
character.  This is why, if you, for example, Googled "Iago," you would get nearly as
many opinions as entries about what his motivates his action in the
play.

It is true that, in the long speech that you cite,
Iago tells the story of being passed over for promotion by Othello in favor of Cassio. 
But, just after he has this long speech, he also tells Roderigo that "there's no remedy"
for his being passed over, "'tis the curse of service" (seeming not to blame anyone, but
to rather blame the way the military works).

And then Iago
goes further in explaining that he only "follows" Othello to "serve [his] turn upon
him."  Here, he explains to Roderigo that he is not one of those "yes" men that do
whatever they must for their superiors in order to win favor.  This point of view, as he
notes in talking about how the military operates, would hardly win him promotion,
whatever else might take place.

But the most telling lines
(57-64) come just after this.  He says:

readability="26">

Were I the Moor, I would not be
Iago:

By following him, I follow but
myself.

Heaven is my judge, not I for love
and duty,

But seeming so, for my own
peculiar end.

For when my
outward action does demonstrate

The native act and figure
of my heart,

. . .'tis not long
after,

But I will wear my heart upon my
sleeve.

. . .I am not what I
am.

These
lines reveal a very important warning from Iago -- a warning to Roderigo, to all the
characters in the play (though they don't hear it), and also to the audience.  Iago is
stating quite plainly here that he intends never to show his true face, that he will
never, in effect, "wear [his] heart upon his sleeve."  His own end, his desired outcome,
is, he says, "peculiar," which suggests that it bears no logic, and, therefore couldn't
be figured out.  But most importantly, he warns everyone that he is not
what he appears to be.

So, in brief, since
Iago has confessed that he cannot be trusted in action or word to represent his own true
feelings, then that means that we, the readers/audience, cannot know his true motivation
or if his story of any event is accurate.

For more on Iago
and truth-telling and Act I, scene i, please follow the links
below.