Thank you to everyone who replied to the list and to me personally.
The general opinion (expressed in varying degrees of politeness) was, as
expected, emphatically NO. I meant exactly the same DNA in both organisms,
and I didn't mean any convoluted definitions of species.
I felt inclined to ask the question after reading 'The Collapse of Chaos -
discovering simplicity in a complex world' by biologist and mathematician
Jack Cohen and Ian Stuart. Penguin. ISBN 0-14-024675-4.
In Chapter 9 they claim that it is indeed (hypothetically) possible for two
completely different organisms to have completely the same DNA. The
justification of this claim is based on the idea that the DNA itself has no
inherent meaning (and so cannot 'define' an organim), but that development
occurs through the interaction of the child DNA and its development
environment (e.g. it's mother's womb).
So two newly conceived embryos with the same DNA but developing in different
contexts (e.g. wombs of females of two different species) would develop in
different ways, producing different phenotypes.
As an analogy we could think of two computer programs, one written for an
IBM compatible PC, the other for an Apple Mac. It's conceivable that these
programs could be exactly the same in terms of the binary string that
encodes them, but because they are run on different computers, completely
different behaviour is produced. The behaviour of the program arises from
interaction of the binary string and the hardware. The behaviour of the
program is not defined by the binary string in isolation. The program could
be debugged by making changes to the hardware that interprets it as well as
to the binary string. Similarly an organism's phenotype is determined by the
interaction of its DNA and the environment in which it has developed.
For evolution this implies that variation occurs through changes in the way
DNA interacts with its context, rather than purely through changes in DNA.
The DNA could be changing considerably in order to keep its interaction with
its context the same (and thus keep the phenotype the same).
I'd be very interested in knowing your thoughts on this. The book I
mentioned is far more eloquent than myself and I strongly recommend it.
Another (more sensational) implication is that we could not clone a dinosaur
purely from its DNA because we don't have any mother dinosaurs who 'know'
what to do with this DNA. The DNA means nothing on its own.
I have also posted the question to sci.bio.evolution.