Could Junk DNA be used as a Turing Machine by nature?
Perhaps this question is whether the regions between genes sometimes known as 'junk DNA' has any function. 

In the human genome, out of ~5 billion bases there are something like 20-30,000 genes which take up perhaps 10s of millions of base pairs, depending on how you count it. 1% of all human DNA is the common figure.   

It is sometimes asked as if biologists commonly think of it as having no use, but in fact this is a researched topic, and few feel that it has no evolutionary or biological function at all. 

Some of the most common uses for intergenic DNA in eukaryotes (bacteria are an entirely different topic with very different responses.


Transcriptional Regulation


Outside the coding sequences of the gene, there can be an extensive set of binding sities for proteins which regulate the gene.  In this paper in Figure 1 the celebrated regulatory sequence of ENDO16 is can be seen in Figure 1. As you can see for almoat 2000 bp there are numerous binding sites for many sorts of promotors and inhibitory factors, as well as factors which may splice the gene in various ways.   

As I recall, ENDO16 only  turns on for a brief period in the development of the sea urchin and so its very tightly controlled, which means that its got a lot of regulatory elements upstream of it, controlling transcription. Its one of the most exhaustively studied genes ever and the believe they have most of it.  Other human genes ive seen perusing medical literature have seen 20kb are necessary to reproduce the regulation of a gene. Still all this might at best only triple the amount of DNA actively involved.


Centromeres and Telomeres
The physiology of the chromosomes have large regions as Deniz mentions are necessary for cell reproduction and for development.  In animals (like humans) the regions are devoid of transcribed genes and might be 10-15% of the genome length (I'm eyeballing this from the UCSC genome browser on chr21 - in some organisms like yeast the centromere can be just a few hundred base pairs.  So anyway we are getting somewhere now!
Non translated genes.
There are lots of pieces of DNA that might be copied into RNA and then do not function as templates for proteins.  some folks say there is a lot of this stuff.  The typical view is that there are a few thousand of these sorts of beasts known, and humans are currently thought to have about 1500 of them.  A small tweak in the number of genes, but they are there nonetheless.
Chromatin binding and organization sites
Although Centromeres are places where chromatin binds, the several families of proteins which bind DNA and wrap them into organized coiled coils thought to be like spools of telephone wire to form the Nucleosome which makes the chromosomes look like the little stick men you see in text books.  Chromatin can spool up just about any sort of DNA but seems to have a preference for regions which are at the ends of genes.  They can be modified by enzymes (acylated, methylated) to modulate their affinity for some classes of DNA sequence.  This is a hot topic of research.  The ability for RNA polymerase to find transcribe a gene is not good if its wound onto chromatin and though its not a precise binding like a transcription factor, chromatin binding and regulation must be affected greatly by changes in the distance between genes and the DNA sequences which surround a gene for thousands of base pairs, which is one of the main differences between species.  


Of all biological systems (at least that I know of) this one accounts for the most bulk DNA sequence and is probably as related to the difference between different species as transcription factors and almost certainly is an older system of gene regulation, if you think about it. 


Copy Number Variations and repetitive regions
just a side note, but small and very long repeat sequences can show up in the intergenic regions as well as inside a gene boundary to account for some of the differences between individuals.  they can be quite short or quite long.  


Well hope this helps?