I'm finding, though, that writing these summaries really helps me review the story and identify where its problems lie. It also helps me highlight the important bits of the story; after all, in a summary, you only talk about the important bits. I think I might have to do this more often for the multi-chapter fics I write.
Will and his coworkers are sent to the London area to work on a collaborative project with another company. During their second-to-the-last weekend there, David joins them to accompany them on their sightseeing. Ben chooses to tour Twickenham, the area they are staying and working in and the town in which Amy grew up.
As they leave the restaurant where they stopped for lunch, Markus takes one of the black cubes that had appeared all over the world a year before, which the restaurant had set out on the tables as centerpieces. Still nervous about what they might be for and what threat they might pose, Ben tries to convince Markus to discard it, but Markus stubbornly refuses, considering it nothing more than a toy. As they are arguing, a bright blue "7" appears on the cube's surface, and the group manages to convince Markus to at least place the cube on the ground far away as they watch the number count down to zero.
When the cube's lid pops open, Markus approaches to see what's inside and goes into immediate cardiac arrest, as do many individuals all around them. As chaos ensues, with afflicted drivers losing control of their cars in the street and causing multiple pile-ups, David modifies Will's mobile with his sonic phone to emit a strong electrical shock and applies it to Markus' chest, bricking the mobile but defibrillating his heart and saving his life. As Ben tends Markus, Will, Amy, and David move on to help other victims in the same way.
As they tend other casualties, Amy screams, pointing out an aeroplane from nearby Heathrow listing in flight and out of control. Pulling off his neural inhibitor, David verifies that the pilots are both incapacitated and the flight attendants are unable to get into the cockpit due to the security locks on the door. Knowing that the effort will likely kill him, he applies his considerable psychic power to stabilise the aeroplane and support it in the air. Amy then hears him in her mind, asking her where he might be able to place the plane safely, and she panicks. Knowing that David cannot hold out forever and noting that he's starting to lose control, Will calms Amy down and talks her through trying to find a suitable landing spot. He then offers his mind to David for support, to help him weather the toll that the effort is taking on him, and together, they move the plane safely to a nearby park. As soon as David is able to release control, he collapses into Will's arms, and the group carries him back to Will's hotel suite. On the way, the cardiac arrest victims who hadn't already died recover.
Once they have laid David out on the bed, Markus demands to know who and what he is and why he was able to do what he did. Will admits that David is an alien and that he's known that for over two years. Markus immediately assumes the worst - that David is a powerful and hostile alien, especially untrustworthy because he has been hiding his true nature - and insists that they turn him in to UNIT. Will counters that David has never shown any ill intention and had, in fact, protected the town from the Judoon, and that possession of power does not mean he intends to use it in a harmful way and does not justify condemning a man for what he has not done. Though he doesn't trust David, Ben agrees with Will, that at the very least, David should have the opportunity to defend himself. Amy is terrified of the man who was talking to her in her head, but considers him a hero for saving the plane, at the cost of his own anonymity and safety, and also agrees with Will.
When David wakes up, its readily apparent that his effort severely damaged his mind, and whilst the damage is still healing, he is barely able to move, understand what people are saying, or say more than a word at a time. Markus demands satisfaction from him, and Amy finally tells Markus that he's being unreasonable to the man who saved his life and that he's not welcome among them. At this, Markus storms out.
After a long while, during which the four watched news reports on the chaos and disaster spread across the world by the black cubes, David tells Ben and Amy his story, in abridged form. They understand that he is simply trying to live a normal life on Earth for a few years whilst he builds his spaceship and agree to keep his secrets, but he informs them that it's too late: Markus will undoubtedly go to UNIT, and David refuses to live his life under surveillance or, if Markus goes to a rogue alien defense group, be captured. In order to cut ties as quickly as possible with these friends that he cares about and doesn't want to see harmed by association, David leaves with the intention of driving back north as soon as the roads are clear to pack up and leave the planet.
Two days later, as Will is heading to work, David surprises him by approaching him in the hotel lobby. As they walk, he informs Will that he did actually leave the planet, and that the events of the past weekend are two years in the past for him. Will realises that this means that David successfully completed building his TARDIS. David invites him to come see the time machine and on the way explains what happened, telling him that he spent the last two years in the time vortex, working on the TARDIS and studying. When Will protests, knowing that David needs his friends, David insists it was good for him. First, without Time Lords or humans influencing him, he found that he had the freedom to figure out who he was. Second, the incident with the aeroplane had hurt him to the point where he had no control over his psychic ability and he could have physically and mentally hurt anyone who had been with him. However, that has all passed now, and he is ready to return to being among people again.
David also explains to Will what happened two days ago (see "The Power of Three" for full explanation). After disposing of the alien threat, the Doctor happened to be at UNIT when Markus reported his alien sighting, and the Doctor took responsibility, telling UNIT that he had lived at that house for a little while during his previous life. He then met David at the house to tell him what had happened and suggest that he flee before UNIT figures out that David is not the Doctor’s previous form. When Will suggests to David that now that the TARDIS is complete, David can travel and possibly see the Doctor more often, David tells him that that won't happen: the TARDIS refuses to speak to David, much less bond with him. He had hoped to travel the universe but was not willing to force the TARDIS to stay with him if she didn't want him, so he plans to release her once he finds himself a place to settle down permanently.
When Will finally gets to see the finished TARDIS, he starts berating her for refusing David, who he argues is strong, clever, brave, and compassionate. David tries his best to defend his beloved ship, saying that he doesn't want the TARDIS if she doesn't want him, and finally breaks down as he's forced to admit out loud that he just isn't good enough for her. As Will's arguments get angrier and more insulting to the TARDIS, the TARDIS begins throwing the two around the console room, but Will refuses to back down. The TARDIS suddenly stills, and as the two men are trying to figure out what's going on, David is stunned as the TARDIS connects with him. He discovers that the TARDIS had always intended to have him but, knowing that he would eventually meet Will, had stayed silent to David in order to test Will, to see how far he would go as his friend. With his ship finally bonded to him, David prepares to travel the cosmos and invites Will to come with him. Though he tells Will that it will be dangerous at times, that he cannot guarantee his safety, and that he might never come home, his friend readily accepts, and the two best mates set off into the time vortex.