"esprit satisfait" doesn't sound right to me, but I don't know how to translate it without a rephrasing like "être satisfait de son sort", so I guess that'll have to do.

d'argent -> de l'argent

t'es -> that's inconsistent with the rest of the register (informal vs casual). If you go that way, you'll have to say for instance "combien de fois t'as entendu dire" and change some expressions for more relaxed equivalents, for instance "ils étaient loin d’imaginer" -> "ils avaient pas idée". In the end that would sound like a guy ranting in a bar after a few beers :)
I would rather stick to basic French, it's a lot less work and the result will sound nicer.
To get a feel of "written informal French"', you could have a look at Renaud, he's got a knack for it. And the song is funny as hell.

combien il est difficile de trouver un homme riche sur dix -> would be perfect without "sur dix" (with a different meaning) but the mix just doesn't work.
"combien il est difficile de trouver même un riche sur dix qui soit content de son sort" or something like that.

ne peux pas -> peut

ne peut pas racheter toute ta jeunesse -> that would be "can't buy back all *of* your youth" (as if rich bastards could buy back some of it!)
I'd rather drop "all of". "ta jeunesse" is quite clear and I don't see a simple equivalent, only a heavy "all that your youth was" or something like that.

Un ami, quand t'es solitaire, ou de paix pour ton âme -> ni d'ami quand tu es seul, ni de paix pour ton âme
I suppose you could say "ou de paix..." but "ni" sounds better, in my opinion

The wealthiest person is a pauper at times
Compared to the man with a satisfied mind -> l'homme le plus riche est parfois pauvre comparé à celui qui est satisfait de son sort

Quand ma vie est finie et mon temps est écoulé -> perfect case of rigid French time consistency. Future is mandatory here

je quitterai -> that's very relaxed French. Only great poets can get away with that :)
You can move the object complement in front of a sentence, it's a very usual way of emphasising it. But the correct way of doing so is to use a "recall pronoun" just before the verb: "Mes amis, je les quitterai".
You can skip the pronoun in spoken French, but writing like that sounds really bad, unless you do it on purpose (for imitating spoken French or some lofty poetic effect)

ce vieux monde à l'esprit satisfait -> "à" makes it sound like it's the world that has a satisfied mind. Just drop the "à" and it will work fine.
for instance "je mourrai content" -> I'll die (a) happy (man)