Hello! I would like to answer this, primarily because I believe the fundamental underlying question itself is flawed. Not due to any problem with the question perse, but rather the knowledge base from which it is asked.
Specifically, in years past (even into my undergraduate studies), the idea of so-called "Junk DNA" was and is still prevalent. However, today it is largely understood that little-to-none of this DNA is in-fact, junk! Much of this DNA, on the order of 50% of the human genome, is derived from transposable elements. These are ancient viral DNA integrations that have become fixed in the human genome and have made multiple copies over the millennia. These are thought to be extremely important for genetic variation and evolution over long stretches of time. The rest of the "junk" are chromosomal structural elements, or are involved in regulating genetic expression.
To your ultimate question, since functionally all of this DNA has some evolutionary role, it is selected for in some way, shape, or form, due to a fitness advantage of its being retained, and the chance of it acting like a Turing machine, wherein the cell would be using these elements to somehow problem solve, is likely zero. Cells rather live or die based on random chance due to mutation providing better fitness and have no real "intelligence" with which to problem solve. And since most of the not-so-"junk" DNA is not protein coding, it cannot be programmed be say, modifying the transcriptional efficiency of its RNA or stability of the resultant protein.
Hope this helped!
