Well since everyone else seems to be too lazy, I'll kick this one off. I'm going to address your article from the athiest side of the conversation, and hopefully create something that can't be discussed further.
Poor categorization. You need to set up a better heirarchy, and this heirarchy needs to logically exclude other possibilties. Let's give that a try:
I. The "universe" does not exist.
1. Pantheism
2. Dream-State (#2)
II. The universe does exist.
1. The universe was created by a nonsentient cause.
A. The big bang.
i. The big bang came out of nothing. (#3)
ii. Some eternal force caused the big bang.
iii. Some noneternal force caused the big bang. (Inifinte loop, devolves to i or ii)
B. Something else that we haven't discovered did it.
2. The universe was created by a sentient cause.
A. The sentient force is eternal (#4).
B. The sentient force is noneternal (Inifinite loop, devolves to A)
3. The universe has always existed. (#1)
A. Always was what it is now.
B. Events in the previous incarnation of the universe caused it to reset (Cyclical Model)
i. Said events were the result of nonsentient causes.
ii. Said events were the result of sentient causes.
Remearkably, we arrive at a total of 11 possibilities, including the loops, and one "something else." It's a lot more complex than the four possibilties you originally gave. And don't even get me started on which minutely differing method to each of those possibilities is right. I don't want to fill up the server's hard disk.
Now I'm going to address each of these 12 possibilities to the best of my ability. This could get lengthy, beware.
I.1: Pantheism.
In the sense that I am using it, Pantheism refers to the idea that there is one being in existence. All of the beings that we perceive in "reality" are merely parts of this superbeing. These facets seem to be self-aware, and not able to utilize the rest of the superbeing's abilities (ie. can't control anything beyond themselves). Beyond this information, it becomes difficult to articulate pantheism, as it loses any distinction between objects and beings, as they are all one.
I.2: Dream-State
This is what you addressed as your second possibility in your article, and I will quote from it during this explanation.
First, difficulty in understanding an argument does not make the argument invalid. I do not understand how to program an airplane. It would probably take me a few months to get a cursory understanding of the code in an airplane's control systems. Nevertheless, the plane works (for the most part) flawlessly.
First flaw in this description: It is essentially impossible to justify that there is another person to interact with. According to this philosophy, you can only prove your mind's existence (supported by Descartes), and thus you cannot believe that anything else is real. It could easily have been the product of your subconscious mind.
There are so many problems with this argument that I'll just start at the beginning. First the athiest ws not clear (shame on him/her!). The imagination did not create the phenomena. The subconscious mind did. That's as much as can be said. Because it is impossible to examine the subconscious mind directly, we have no way of knowing why or how the phenomena were created. Next, quotes from John Locke are not infinitely perfect. Nor from Thomas Hobbes, the Baron Montesquieu or any other other philosopher. Hallucinations disprove this one. A hallucination is a jumble of all sorts of stimuli that have been mashed togther and fed to the visual processes. Also, since we are looking at subconscious processes, not conscious processes, they are not tethered to linear thinking, which produces "distortions." We have also seen computers generate things that are completely unique using genetic algoriths.
And just for kicks, here is a story that gets pretty darn close to uniqueness:
everything2.com/title/unbelievable%2520scenesII.1.A.i: The Big Bang came out of nothing.
As you stated in your article, something cannot come out of nothing. So that closes it for this avenue. But I'm going to take this section to prove that the Big Bang could create this universe, so that all I have to do is prove that the Big Bang could happen later on.
If you take every rock on the planet, cut a 1 cubic foot block out of each one big enough, and then go and look at all of the sequences of atoms, you will see many more combinations than are in DNA. DNA combinations can be created just by the forces of nature combining the elements by chance. There is absolutely no scientific reasoning to refute the idea that a DNA pair can be created by a certain chance set of events. We have good reason to believe that the required elements were present on earth in primordial times.
We can show that fundamental amino acids can be made by lightning from those precursor chemicals.
As far as the survival of these "chance" organisms, yes, many of them probably died. But the survivors, well, survived. They passed on what gave them success, and those traits subtly modified through evolution, which has been amply proven.
Please actually read your sources, rather than just parroting off comments taken out of context. The full quote is available
here. Darwin was using a common writing device, where the author concedes that his position seems absurd, then goes about methodically explaining it and deconstructing the arguments against.
Secondly, "accident" is an improper term to describe any natural process. Accident implies that something was being attempted by a thinking being and that something else happened that was not supposed to. The formation of all of the things in the universe happened according to natural laws, not a thinking being. And don't even get me started on your earth orbit nonsense. The
Habitable Zone of the Sun is approximately 39 million miles wide, or almost 5,000 times the diameter of Earth. The earth also moves farther away and closer to the sun in it's orbit, so even if you don't buy my Habitable Zone argument, you have to go with that.
Moreover, there are more stars than we can count out there, and life only has to evolve on one of them. If life were unable to evolve on Earth, we wouldn't be talking about this right now, you'd be telling me how the features of Quogalash are perfectly tuned to our life. And I'll finish this off with a short
quote from Douglas Adams:
II.1.A.ii: Some eternal force caused the Big Bang.
This happens to be my viewpoint, so I may soapbox a little more in here than the others. You have been warned.
Now that the post-Bang stuff has been cleared up, let's return to causality. THe Big Bang can't come out of nowhere, so it must have come from something. Now,
St. Thomas Aquinas tells us that everything must have an ultimate eternal cause, and unmoved mover, etc. I'm going to accept that, mainly because it just makes sense. But where I draw the line is jumping from that to God. There can be an eternal causative force without it having a mind, will, whatever you wish to call it. This force is the
Zero-Point Energy Field. This is an inifinite sea of energy underlying the fabric of reality. As far as we can tell, it has always been there. There is absolutely no evidence to show that this field has any sort of will or mind. This is what caused the Big Bang. A seepage of energy from this field created the universe.
This is a fact. This is not just an issue of the Big Bang theory, the universe is expanding and we have
proof. Now to deal with you misconstruction of the big bang theory. First of all, baseball is way too big. We're talking everything compressed to a sphere of one Planck Length in diameter. A Planck Length is about 0.000000000000000000000000000000000016 meters long. Or if you prefer, 0.00000000000000000000000016 nanometers. Next, matter doesn't exist before the Big Bang, or even for a short time afterword. You're looking at pure energy here. The
Law of Conservation of Mass/Energy states that the total amount of energy in a closed system remains constant, and that mass is merely "frozen energy" via E=mc^2. The reason for the expansion is the influx of energy from the Zero-Point Field. It's not going anywhere, in the same sense as evolution, because it's just going forward, wherever forward happens to lead. Like a giant wheel rolling down a hill, it goes, not to get anywhere, but it goes until it stops.
II.1.A.iii: Some noneternal force caused the Big Bang
As I commented back at the start, this is a loop. Accepting Aquinas' view, a noneternal force requires a creator, ad infinitum until you get to an eternal force. That wraps it for this one.
II.1.B: Something we haven't discovered did it.
Can't really do anything for you here. Just noting that we probably haven't exhausted the possibilities in this category.
II.2.A: The sentient creator is eternal.
Basically here's a God button. The problems with this view: Occam's Razor and zaps to Pantheism.
Occam's Razor:
Both this and the nonsentient eternal force result from the same reasoning. There is nothing concrete to distinct between them. However, William of Occam proposed for us Occam's Razor, which states that the solution that demands the fewest assumptions is most likely to be true. We have a theory which is in all degrees demonstrated to be possible (Nonsentient Eternal), but we can't go back and watch the beginning of the universe so we can't verify it. Then we have the God theory, which adds the assumption that a necessary being would have a will and a mind. Occam's Razor says trim the assumption.
Zaps to Pantheism:
The fact that you have an infinite being raises problems when the theist assumes that their God can interact with the physical world. An infinite being cannot have limits. Therefore, anything it interacts with it must consume. Everything must then be a part of God, because God has interacted with the universe under the theist's system. Thus you have Pantheism.
II.2.B: Sentient creator is noneternal.
Same problem as with the other noneternal. That about covers it.
II.3.A: The universe has been the same as it is now forever.
Giving credit to you, you actually got this one pretty much right. Thermodynamics says this is impossible.
II.3.B.i: Nonsentient causes in the last universe created this one.
Basically this is the old idea of Big Bang/Big Crunch. Not a lot of weight given to it now, but it's not been fully ruled out.
II.3.B.ii: Sentient causes in the last universe created this one.
I'm not going to really explain this one, sufficed to say it is in the realm of science fiction. But it's not necessarily impossible, so who knows?
This story gives a pretty good example of what I'm talking about.
I personally love the debate and love to do research and find more and more ways to make atheists backslide. 
Not to be rude, but rather to be a soldier for God 
