The Urey-Miller experiment of which you speak has been discredited for some time. The couple of amino acids that resulted were far simpler than the basic building blocks of life, and used a precursor "chemical soup" that has since been determined to be completely unrepresentative of the condition on earth at the time life is posited to have begun. That is why the OOL question is still completely open, and why virtually no hypothosis currently put forth has gained any traction or proved to be fruitful in guiding further research. Each such hypothesis results in more questions than it answers, intractable questions that continue to stymy progress in OOL research. Even if scientists managed to produce simple amino acids with the chemical compositions actually available in pre-biotic earth, this is still so far from true life that it is naive in the extreme to assume that would lead inevitably to DNA-based life. Life cannot exist without the DNA code of life, yet DNA would not exist in the absense of the basic components of cellular life. The simplest cell possible is so vastly complex and specified that the odds of it happening by chance exceed the probablistic resources of the entire universe since the moment of the Big-Bang. That is a basic tenant of intelligent design theory, not (as those wishing to label it "creationism" would like you to believe) scripture.
Why, might I ask, is it scientific to look at forensic evidence, or rock formations, or EM signals from space and ask, "Is it natural or designed?", but un-scientific to look at the incredible complexity and specificity in a single living cell, or the fine-tuning of the cosmological constants, and ask, "Is this designed?" Who the designer is may be a question not answerable by science at this time, but detecting the hallmarks of design itself certainly is not.
Ooooh!. I love the irreducible complexity argument. Reeks of desperation. It's like that guy the cops are putting the screws to under the heat lamp; he keeps changing his story. First it was, "God made Everything in seven days just like the bible says." Then we have,"Ok. Ok. Seven days could mean any amount of time to The God. He just buried all those fossils and such out there to test our faith while we're surrounded by you blaspheming ape lovers." Now we have, "Just Look at the flagellum! All those little parts don't do anything on their own! They cannot have evolved individually. Jesus put them there. Now let's call it Intelligent Design (Yup, just like that with capitol letters to make it sound all official-like), and maybe we'll fool some folks that are sleeping.
You see, legitimate science is trying to figure out what happened without making any assumptions. Creationists and intelligent design enthusiasts think they already know what happened, and they are desperately looking for any way to prove it. And ruling out the possibility of a designer is not good science either. There may very well be one. If so, that doesn't change the fact that favorable gene mutations survive ,etc.,etc.
EDIT:
The simplest cell possible is so vastly complex and specified that the odds of it happening by chance exceed the probablistic resources of the entire universe since the moment of the Big-Bang.
I just read this part again, and WOW! Not only do you creationist types claim to know the odds of the first bacterium forming, you also are privy to the total potential of the entire universe! Powerful knowledge, indeed! Too bad for evolutionary proponents that this isn't being hashed out in a court of law. That info would be the first thing requested in pre-trial discovery!