I don't know the truth about this either way (though I'm leaning towards the growth model), but I think some of the arguments in favour of innate ability that have been posited above are flawed.
First of all, 'success' is not the same as 'talent'; there are lots of seemingly talented people, with 'spark', that are not successful in their chosen field and vice versa.
Secondly, in order to be gifted at, say, music, it is not necessarily the case that a person is innately able; it's also not necessarily the case that they have spent hours upon hours working on that particular skill. Other skills could conceivably build up the required neuron pathways, so they could appear to be geniuses when in actual fact the skill is very much learned - but in other contexts. IYSWIM.
We know that genetic variation exists and manifests itself in our 'hardware', and obviously lots of people are limited by the hardware they end up with. Some people, on the other hand, have the perfect hardware required to do the job. That, along with dedication, is what we term 'sporting talent'.
The growth model rests on the assumption that we all have the same 'intelligence hardware' at birth. The crux of the matter, and the reason we can't answer this definitively at this point in time, is whether or not intelligence is a function of your 'hardware', or whether 'software' is more important.
To labour the computer metaphor further, I think it's probably a bit of both. Hardware limits software. You can't run Windows Vista on an old BBC computer.