OK, gotta put in my 50th of a buck.
The OP asked about artistic talent (is it inborn) and then continued to ask if anyone can become an artist. “Talent” in most people’s minds is innate, inborn ability, so yes, talent is inborn. The unspoken assumption is that talent is necessary to become an artist–ah, there’s the rub.
Having inborn talent makes it easier to get anywhere in life, but it’s not the be-all or end-all of what gets you there. There are abundant examples of highly talented people who got nowhere. Equally abundant are the people who are less than talented who made a name. On the third hand, being famous doesn’t make you an artist in any field (hence multiferous Cafe Society threads about “is XXX any good?”).
There are whole courses in art programs that try to define what makes “art” and what makes an “artist”–with varying degrees of success. Much depends on what you’re planning to do with the definition. Do you want to disqualify something you hate from being “art”? Do you want to look down your nose and say “But I prefer real art”? Do you want to provide funds, but only for “art”?
I have a talent for mathematics and mechanics, and I make a living as an engineer. I’d rather be playing the guitar, and I have been since 1966 or so, but I don’t have a lot of talent for it. Playing the guitar don’t pay so good, either, and I have kids to support. When my band gigs, people always say “You have such musical talent!” Hogwash. I ENJOY playing. Sometimes other people enjoy my playing also. Am I an artist? My wife is a talented painter who sells one of her (abstract) works every once in a while for $500 or so. She teaches art at the local college. She’s an artist. She does not consider the ability to draw a nose properly to be an “artistic” talent–that’s simple visual and mechanical ability.
So, OP (I notice captainQwark has not contributed lately) why did you ask your question? Do you have an untalented child who wants to be an artist? Do YOU want to be an artist? Are you defining “be an artist” by financial success, critical approval or personal, deep-down satisfaction? Let us help you!
As a visual artist I’ve spent 8 yrs of college and 6+ professional years to get where I am ability-wise, so I do feel a tinge of annoyance when I’m told I’m “gifted”.
Of course some people are going to be more adept at any given task than others. Heck, look at how people drive.
But so much of art (traditional, visual art at least) is learned. Color theory, perspective, composition, etc. And like anything else, these skills are only refined by practice and feedback.
Not that people can’t create beautiful things without training. For instance, there’s lots of Folk Art that is really quite beautiful. But just like a person may be able to learn how to drive a car by trial and error, you’d probably save yourself a lot of time and trouble by taking a lesson or two.
Seriousart, you should post your work in the Teemings art gallery. 
Well, I’ll offer myself as an example. I’ve received almost no instruction what-so-ever (a couple of years of high school art class to mooch supplies; I dropped out of college after about a month, I’m 23 now) – I have been making “art” my whole life, but I am almost entirely self-taught. I pick things up – paints, markers, pencils, whatever, and know how to use them. I just always have.
You know how some people ask little kids what they want to do when they grow up, and every day of the week they give you a different answer? My parents have stuff I drew when I was 3. I’ve said I was going to be an artist my whole life.
It’s just a thing I do. Interpret it however you like.
Oh yeah, I also write, sing, [used to] play the violin/viola, trumpet, and piano too, but there aren’t enough hours in the day or money for me to pursue all of them anymore. I was always first chair in my music classes. 
Anyone want to give me a grant?
Actually, I sent some stuff off to Euty a couple weeks ago, but we had some file compatability issues. If all goes well, I’ll send some more stuff today. I’ll post when they go up. It’ll be interesting (scary) to see what people think.
But heck, if art school does nothing else, it’ll give you tougher skin for criticism.
Who’s surprised? I never said I was surprised by my lack of musical ability, or my sister’s inability to break down an object to its simplist shapes. I know they are separate abilities, that was part of the point: that talent in one artistic area does not equal talent in another artistic area.
The OP simply asked if one is born with talent. I was trying to illustrate my opinion that one is born with talent by comparing my talent to my sister’s talent and showing that we cannot get the hang of each other’s talent regardless of study.
But what if I don’t want to read a site about savants? 
Besides, I don’t recall saying that intelligence has anything to do with it. In fact, by stating my sister’s intelligence, I thought I was making the point that intelligence had nothing to do with it. It’s something you’re good at or you aren’t. Like reading comprehension I guess.*
*just teasin’