To start, I'll bet you that whatever apparently (hi Sabertooth) random initial DNA sequence would result in a viable life form in any conditions on earth. My chances of winning are extremely small, as the math shows.
However, over a billion years, I wonder how many DNA sequences tried and died because they didn't result in a viable life form? Something with a very high exponent I'm sure. Enough tries to even out the odds? What we see are the results of the tries that worked.
If your DNA sequence (that you refer to above) is longer (counting sequential base pairs) than a sequence equivilant to 96 letters in the English alphabet, then the math shows that it can not happen randomly in 17 Billion years of trying.
The sequencing of any data over that size must be done by a non-natural process, per the math in said proof.