The initial situation is the set-up, the part of the story where we learn the basic background that sets the plot in motion. In the first chapter, we learn that Davie is poor, recently orphaned, and looking to make a living outside his hometown of Essendean. His friend Mr. Campbell advises Davie to go visit Davie's relatives at the noble house of the Shaws.
All Davie's hopes of having great, noble kinsmen are completely shattered when he arrives at the house of Shaws and finds it in disrepair and inhabited by one guy, his uncle Ebenezer Balfour. He also discovers that his uncle's kind of crazy: Ebenezer keeps insisting on locking Davie in his room, and he won't come clean with Davie about his relationship with his brother, Alexander – Davie's father.
This stage is the part where the conflict gets more intense, and it doesn't get much more intense than attempted murder (except maybe actual murder). Ebenezer sends Davie out at night to a tower at the side of the house with an incomplete staircase, from which Davie barely manages to avoid falling. This effort to kill Davie and make it look like an accident convinces Davie that his uncle has some strong reason for wanting Davie out of the way. Davie believes that the issue is that Davie's father was actually older than Ebenezer. Why does that matter? Because if Alexander (the father) was older than Ebenezer, that would make Davie the rightful heir to the house of Shaws. So Davie demands answers from his uncle, which Ebenezer promises he will provide in the presence of his lawyer in Queensferry the following day.
The climax is the end of the set-up of the plot, the moment when everything comes to a head. In the case of Kidnapped, that happens relatively early in the novel, in chapter seven. Ebenezer lures Davie into the town of Queensferry with the promise of a visit to a lawyer. But instead, he brings him to a ship, the Covenant, and leaves him there, to be sold into slavery in the Carolinas. Everything that happens after this – the shipwreck, the meeting with Alan, the flight across the Highlands, all of it – belongs to the next plot category.
We've got the set-up out of the way: we know that Davie is the heir to the house of Shaws, that his uncle is a stealing bastard, and that Davie has to get back there to claim his inheritance. But how? Since this is, again, an adventure story, the great bulk of the novel is given over to the "Suspense" plot stage, when it's clear that the narrator knows what's going to happen (after all, the narrator is the future Davie) but we don't. All of the stuff that takes place between Davie's forced departure from Queensferry and his eventual return after two months of dodging British troops and Campbells in the Highlands comes under the heading of suspense.
In chapter 28, after about 22 chapters on the road, Davie finally gets his promised conversation with Ebenezer's lawyer, Mr. Rankeillor. At this point everything is cleared up and we find out that Davie does have a legal claim on Ebenezer's property.
In "What's Up With the Ending?" we mention that there isn't much of a conclusion to the novel. But there is a conclusion to the specific plot arc of Davie's inheritance. Alan visits Ebenezer, posing as a Highlander who is holding Davie hostage, and manages to get Ebenezer to admit that he had Davie kidnapped. Mr. Rankeillor and his clerk are both hiding there as witnesses. They threaten Ebenezer with legal action unless he promises to give over two-thirds of the income from the Shaws estate to Davie from now on. Alan's future remains up in the air, but maybe that doesn't matter. Maybe Alan's Highland uprising business is just there to add suspense to the adventure portion of the novel.