It sounds like the event you are looking for to tie the components together into DNA is similiar to getting a monkey to type a novel. You can get a computer and buy a monkey and bring them together to the point where the monkey actually starts typing on the keys. But to go from that to a readable novel is another story.
Unless the monkey's typing matches some agreed upon context as to what the charater combinations mean, the typing is rambling nonsense. In order to get an agreed upon context you need an infusion of intelligence and that is very hard for me to see happening by chance, since DNA strands are the characters of an assembly language on how to build something. Your model leaves even the creation of intelligent infusion to random chance and that's an even greater stretch or leap of faith to me then the self assembly of DNA to start with.
In other words, even if the DNA could create itself through random chance and time, what is this stuff supposed to do with itself once it comes into being without some force guiding it's implementation?