To open things up a bit ask yourself, what does DNA do? Is it possible to enlarge our understanding of "computation" by thinking deeply about this?
[WS:] I am not sure where you are heading, but let's substitute the word DNA with the word abacus in your argument. What does the abacus do? If the beads in the abacus move, e.g. powered by some external force (gravity, wind, or for that matter muscles of a living organism), does that mean that it is computing? As I see it, it does not, even if it is possible to discern regularity in those movements. It is only when the human mind interprets those movements as concepts when computation occurs. Ditto for DNA and any other natural process. It is so, because I believe (as Kant did) that it is an inseparable gap between reality and a representation of reality in the human mind.
Computation, or for that matter, any manipulation of ideas is unique to the human mind, even though it corresponds to natural patterns. It is, however, quite possible that the same patterns would have a very different mental representation by an organism with very different cognitive capacities than ours. That is not to say that the order in reality is human creation (a subjectivist position), but rather that it s a thing in itself or noumenon as Kant called it (http://en.wikipedia.org/wiki/Noumenon) which is accessible to the consciousness only as an image (phenomenon) created by that consciousness. Therefore the same noumenon can be imaged as different phenomena if perceived by organisms with different cognitive capacities.
Assuming that computation i.e. the human way of manipulating information and creating phenomena is natural is tantamount that ours is the only, or perhaps 'privileged' way of perceived the world. That is a quite grandiose and arrogant position, indeed. One does not need 21st century computers to propose that, -neo-classical economists believed that long time ago :).
Wojtek