I am certainly no expert on this, but I will throw my 2 cents worth into this discussion. (Besides, when has a lack of expertise been grounds for not commenting, here).
Hadriel seems to be focused on the step from an RNA world to a DNA world, and how could that have occurred.
We know RNA based lifeforms could have existed in the past, because they still exist in the present. For example, picornaviruses (such as Polio, various forms of Hepatitis, common cold, etc) are just self-replicating RNA, in a protein shell. They have no DNA. The reason that they mutate so fast is that RNA is less stable than DNA. You might think that they need a protein shell to survive, but I recall reading that even an RNA strand on its own has proven to be "contagious" and dangerous.
Even simpler than picornaviruses are "viroids". They are basically RNA lifeforms that do not even have a protein shell or even produce any protein. You could argue that they are not living things; just a complex chemical molecule that has a certain shape that tends to duplicate itself over and over, if in the right environment.
More complex than viroids and picornaviruses are double-stranded RNA viruses (eg gastroenterisis), which (my guess - I am no expert) could have evolved to the first DNA viruses. Or the intermediate step in the evolution to DNA viruses could have been through something similar to a retrovirus (which is self replicating RNA but uses DNA as part of the process).
So there you have it. Simple RNA lifeforms that dont rely on or make any protein, slightly more complicated RNA lifeforms that DO make protein, still slightly more complicated lifeforms that are essentially RNA but use DNA as part of the process, other RNA lifeforms where the RNA is arranged in a very similar way to DNA. All these lifeforms living on earth today. They are not science fiction.
The point I am making is that, although the exact route from an RNA world to a DNA world is unknown, the mystery is NOT that it couldn't have happened, it is which of the many possible ways it could have happened, did it happen.
Oh, and in relation to abiogenisis, coding, and the monkey typing out Shakespeare analogy, I recall reading somewhere that in a lab they have been able to create a self replicating RNA with a chain of only 120 or so "characters". you might think that even getting 120 characters in the correct order is unlikely. However, it only has to happen once, there are multiple orders that will self replicate, and that keyboard only has 4 keys on it.