Early the next morning, Harry buries Moody's eye under a tree. Later, they decide to move on. They camp near a village where Harry can grab food, but he returns from his quest panting and explains that the village was teeming with dementors and he couldn't make a Patronus. Ron is furious that they don't have food, but Hermione interrupts his ranting and tells Harry to take off the Horcrux. As soon as Harry does, he feels light and free. He insists he wasn't possessed, but still believes that they need to wear the locket for safekeeping. They decide to take turns wearing it.
It's important to keep in mind that, because they're on the run and don't want to endanger any of their other friends by reaching out, Harry, Ron, and Hermione are now the only social contact that they have—a situation that, in the long run, is untenable. That the Horcrux makes them irritable and less accomplished continues to drive home that the immortality it represents is in direct opposition to life and friendship.
The trio moves to a field and Hermione steals eggs and bread from the nearby farm. They discover that eating well means their journey is bearable, while Ron becomes unreasonable when there's no food. Ron constantly asks where they're going next and broods over their food situation while Harry and Hermione list the places where Voldemort might have hidden Horcruxes. Ron continues to be snappy about using Voldemort's name, and Harry continually insists that Voldemort hid one at Hogwarts. Harry knows it was an important location for Voldemort, but Ron disagrees.
Ron's behavior in particular continues to drive home that only ever seeing two people isn't going to work out long-term: at some point, the trio will need to make contact with others if they want to accomplish their goal. Harry's sense that Voldemort hid a Horcrux at Hogwarts suggests that he understands that Hogwarts is a place where misfit children can find a home; it would represent belonging for Voldemort, just as it does for Harry.
Harry's scar keeps prickling. Though he shares with Ron that he continues to see the thief that stole from Gregorovitch, Ron is disappointed that Harry can't see anything else. Harry begins to suspect that Ron and Hermione talk about him when he's not nearby, and he wonders why they came in the first place. Ron is constantly angry, and Hermione seems disappointed. As the fall wears on, Ron's mood continues to worsen. One night, he insists that Mrs. Weasley can make food appear from nowhere, which Hermione explains is impossible. They begin to shout at each other until Harry tells them to stop—he hears someone.
As the weeks wear on, all three of them become increasingly testy and vulnerable to attacks from each other—another consequence of being each other's only contact with other people. That Ron has such a difficult time makes it clear that this journey isn't at all straightforward and simple; it's one in which Ron will have to make peace with the lack of solid information, just like Harry is trying to do with Dumbledore.
They quietly listen to what sounds like several people climbing down toward the riverbank. Hermione pulls out Extendable Ears and hands one each to Ron and Harry. The newcomers catch salmon, and Harry hears a language he doesn't recognize. They discover that there are two goblins, Griphook and Gornuk, in addition to Ted Tonks, Dirk Cresswell, and Dean Thomas. Ted asks the goblins why they're on the run, as he thought the goblins supported Voldemort. The goblins explain that they don't take sides, but they were asked to do things that were below them and that Gringotts isn't under goblin control anymore.
The fact that Gringotts is now presumably controlled by the Death Eaters shows the trio that Voldemort seeks to subjugate everyone in the magical community, not just Muggle-borns and Muggles themselves. This does suggest that, while Voldemort might think little of house-elves, he does recognize that goblins aren't beings to mess with—they should be subjugated, not ignored.
Griphook laughs and makes a joke in Gobbledegook. Dirk and Ted discuss that, at Hogwarts, Ginny and some friends tried to steal the sword of Gryffindor from Snape's office, so he sent it to Gringotts. Griphook laughs and says the sword is a copy, and then says indifferently that the students were punished. They discuss whether or not Snape killed Dumbledore, and both Dean and Ted defend Harry and tell Dirk to read the Quibbler to get the facts. A few minutes later, the party moves away.
Learning that Ginny tried to steal the sword shows Harry that the resistance movement is still alive and well at Hogwarts, something that likely makes Harry feel less alone. This will be one of Harry's early indicators that he needs to expand his community and let others in; doing so gives him hope, a necessary ingredient as he continues along.
Hermione digs Phineas's portrait out of her bag, reasoning that he might've seen someone swap the swords. As soon as he appears in his portrait, she blindfolds him. He's incensed, but he reveals that Neville and Luna helped Ginny, and that all three served detention in the Forbidden Forest with Hagrid. Hermione asks if the sword has been taken away for cleaning, but Phineas laughs at her and says that goblin-made weapons absorb things that make them stronger and repel dirt. He starts to leave and says that he last saw the sword out of its case when Dumbledore used it to break a ring.
Drawing on Phineas shows that Hermione is beginning to put together that she needs to pull from a variety of sources as she figures out what's happening and how things function; this is especially important given that Phineas is a Slytherin headmaster and, therefore, is, according to Harry, less likely to want to help a Gryffindor overthrow the current Slytherin headmaster.
Harry and Hermione celebrate as Hermione shoves the portrait back into her purse. They deduce that Dumbledore planned to use the sword on the locket, but they wonder where Dumbledore hid the real sword. Harry turns to Ron for an opinion, but Ron meanly says he doesn't want to spoil their fun. He spits that he's cold, hungry, and feels like they're not accomplishing anything. He insists that Hermione is disappointed too and Harry tells Ron to go home if he's finished. They draw wands, but Hermione conjures a shield between them. Ron throws off the Horcrux, accuses Hermione of choosing Harry, and storms off. Hermione tries to chase him, but he Disapparates.
As far as Ron is concerned, having the information that they need the sword to destroy the Horcruxes isn't actually useful when they have no idea where the sword itself actually is. Again, the fact that he feels this way when he's wearing the Horcrux shows how being so close to this poor attempt at immortality makes Ron less interested in actually living and making his own life and the lives of others better by trying to figure out how they can get the sword.