DNA is a biological means to code, store and reproduce data. So is a book. Neither of them are analogous to computers. In biology, each three consecutive triplets of nucleotides codes for an amino acid (codons). String enough amino acids together, in the correct order and you have a protein. This is not what the researchers are looking at.
DNA is a (relatively) stable molecule that can be made very long. The sequences of nucleotides can be "read" by sequencers. Unlike, biological systems, your code could be represented by codons of 3, or 4, or 5, or 20 nucleotides.
The difficulty is two fold. Currently, artificially made DNA is not able to be made in sizes comparable to our chromosomes. Also DNA is not totally stable. There are many ways in which DNA strands alter themselves. Therefore the program, that decodes the DNA, must have a good "fudge factor" built in to compensate. (Just look up DNA mutation to see how many things can go wrong). Plus, in biological systems, there are built in DNA repair mechanisms to keep on top of many of the mutations.
Think of a substitute barcode system that uses organic molecules instead of black lines and spaces. You could probably use proteins as data retrieval and storage systems too. Proteins are not as good. They tend to fold into very complex patterns making their "readings" difficult. Plus, biological proteins are made up of 20 different amino acids. DNA is much simpler, consisting of 4 nucleotides and 1 sugar. It's also easier to unzip and read.
