Since first Adleman experiments many advances has been made, and various Turing machines has been proof to be constructable.
They are works over one dimensional lengths, bidimensional tiles, and even three dimensional DNA graphs processing.
At 2003-2004 there is no known application for DNA computing that is able to his incredible parallelism capabilities. The input/output interfaces still slow and expensive.
The DNA computing technology is related to the micro mechanical technology (that also use DNA for structural and mechanical constructions) (switches, gates, etc...).
Slashdot article: http://slashdot.org/article.pl?sid=00/04/19/0858252