So we've just witnessed an impossible event, as the Doctor we knew and loved appeared to change in front of our eyes.
The Power of the Daleks picks up right where we left off, and even though we know that William Hartnell isn't coming back, we're still uncertain just as to who this strange new man is. And the story, rather than trying to reassure us that no, this is the same man, seems to gleefully make us doubt even more. Other than a moment with a mirror, where Patrick Troughton momentarily sees his previous version, and a bit of dialogue here and there, there's a concerted effort to wrongfoot the audience, as well as the Doctor's companions. They make it a point to show that the Doctor's old things don't fit the new Doctor anymore: his cloak threatens to strangle the new man, and the Doctor's ring is much too big. And this new version keeps referring to the Doctor in the third person, with lines like, "The Doctor was a great collector, wasn't he?" and "The Doctor kept a diary, didn't he?" It's a bold move, making the audience as uncertain of what's going on as the characters in the story, and even the provided explanation isn't as much help as it seems: "I've been renewed. It's part of the TARDIS; without it I couldn't survive."
And then they take this strange new character and insert him into a story about an isolated Earth colony. But unlike the previous story, this isn't a base under siege from outside forces; this is a colony with its own internal struggles (there are mentions of rebels and political factions), and one into which a dangerous element has been introduced: the colony's scientist, Lesterson, has discovered a space capsule in the mercury swamps. The Doctor gets mistaken for an official from Earth called the Examiner, and so he discovers what Lesterson has found: a capsule containing Daleks -- Daleks which might not be as dead as initially thought...
Episode two finds us moving a little further along. The presence of the Daleks throws things into sharp relief: we may not know for sure if this is still the Doctor, but he stands opposed to the Daleks just like the old Doctor would, so we can't help but trust in him. But what's fascinating about writer David Whitaker's approach here is that, unlike in previous stories where the Daleks are introduced at the end of the first episode and then fully unleashed, here the Daleks remain both in the background and the focal point of the episode. The Daleks seen here don't have any power, so we see instead Lesterson's efforts to bring them back to life. The Doctor, in his assumed role as the Examiner, demands that the Daleks be destroyed, but no one is willing to listen to him: "You're exceeding your authority," Lesterson says. And so while the Doctor is trying to get someone to order the destruction of the Daleks, Lesterson manages to bring one back to life.
This leads to the climax of the episode, when a Dalek glides into the meeting room where the Doctor is talking to Governor Hensell. The Dalek seems to recognize the Doctor, focusing in on him, and we finally believe that yes, this is in fact the Doctor, the same basic man as William Hartnell. But then, as the Doctor tries to convince the colonists of the Daleks' nature ("The thing it does most efficiently is exterminate human beings. It destroys them, without mercy, without conscience"), the Dalek begins chanting, "I am your servant" over and over, drowning the Doctor's warnings out, and you realize how devious these Daleks are...
