Who or What is the Gospel of John Talking about in John 1:9-13?

I will quote from the New International Version, which makes this passage into a paragraph:
"9 The true light that gives light to everyone was coming into the world. 10 He was in the world, and though the world was made through him, the world did not recognize him. 11 He came to that which was his own, but his own did not receive him. 12 Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God— 13 children born not of natural descent, nor of human decision or a husband’s will, but born of God."
This seems to be structured to be a tie between three different themes, in John, first, this power or force of influence, the Logos, that can bring things about, second, the person, John the Baptist, who has this logos in him in the form of Light, and third, the person Jesus.
What I want to do is to dissect this a bit, to pull apart which sections of the narrative is talking about which of these three things. This is not a simple thing to do, so I want to start out by just saying what my intention is, and to say what I think these parts are, and later I will be supporting this view with what I think is evidence that comes from what these words actually mean in the Greek of the original version of the text.
If you did not know anything about the Greek that this Bible passage comes from, but just read the translation, you might take what they are trying to say by how they translate it as the obvious correct understanding of it. What I propose is that what is being promoted by this intentional angle in translation is something that religionists are forced to do in order to support accepted church doctrine and dogma about the Trinity. Why I very early on decided this is the case is from going onto online discussion forums and seeing in the religion section of the forum, arguments being made for and against the Trinity doctrine, and how without this particular interpretation of John 1, there is no real argument on the dogmatic side.
An overview of what John is actually talking about, I will briefly cover in this post, which is that John, talking to Greeks, is not like the other three gospels using an argument that these events had to happen because it was so prophesied. Instead, he introduces a thing he calls logos, which is a thing that is somehow behind events, starting out with why the world even exists in the first place. Then, the writer of John goes on, once there are people here in this created world, this logos takes the form of enlightenment so people can live well.
Where it gets tricky is where the next step is to say this light came on and the world refused it because of not accepting or recognizing it. I think this is the key point where people sort of fall off the cliff and stop following along with John. I think the translators use an interpretation created by a forced bias, one to support doctrine, to make you think without saying so that this is talking about Jesus being literally the logos and his being eventually killed. I have to say that if you look at it objectively, you have to go back to my first basic premise that it is talking about prophecy. You have the Law and the Prophets, which would have lots of meaning to Jews, but not any to Greeks. So here it is saying in a understated way for the sake of those Greeks, that this light came through the Law and the Prophets to the Jews who should have benefited from it to gain enlightenment but it was shut down and instead was built into a institutional thing to support what had become basically a business of getting people to come to their temple.