Power of the Daleks was Patrick Troughton's first story as the rejuvenated Doctor, and he underplays his role, letting the audience wonder like Ben and Polly whether this man is really The Doctor as we knew him ...
None of this story survives. It happens to have a fine supporting cast. If we check IMDB and look for the cast's appearances around this time, in shows that have had a good life on video, we get a few leads. In a moment, we'll be following those leads ...
Anneke Wills (Polly) has of course been covered in her own thread.
http://www.who3d.co.uk/forum/index.php?topic=1317.0Robert James
"Steptoe and Son" Upstairs, Downstairs, Upstairs, Downstairs 20 October 1974 (Season 8, Episode 5)
"The Avengers" Death a La Carte 21 December 1963 (Season 3, Episode 13)
"The Avengers" Too Many Christmas Trees 25 December 1965 (Season 4, Episode 13)
The Avengers" Look - (Stop Me If You've Heard This One) But There Were These Two Fellers... 8 May 1968 (Season 7, Episode 11)
Partly Missing: "The Avengers" Hot Snow (1961) 7 January 1961 (Season 1, Episode 1)
Missing: The Avengers" Brought to Book 14 January 1961 (Season 1, Episode 2)
Peter Bathurst
"Doctor at Large" Trains and Notes and Veins 18 April 1971 (Season 1, Episode 8 )
"Doctor in the House" All for Love... 26 September 1969 (Season 1, Episode 12)
"Doctor in the House" Why Do You Want to Be a Doctor? 12 July 1969 (Season 1, Episode 1)
"Moonbase 3" Castor and Pollux 7 October 1973 (Season 1, Episode 5)
"Moonbase 3" Achilles Heel 23 September 1973 (Season 1, Episode 3)
"Moonbase 3" Departure and Arrival 9 September 1973 (Season 1, Episode 1)
Peter Bathurst also played Chinn in Doctor Who: The Claws of Axos, which is worth looking at.
Pamela Ann Davy
"The Saint" To Kill a Saint (1967) 24 February 1967 (Season 5, Episode 19)
The Avengers" The Living Dead (1967) 22 February 1967 (Season 5, Episode 7)
The Avengers" Mission to Montreal (1962) 27 October 1962 (Season 2, Episode 5)
Nicholas Hawtrey
"Danger Man" Don't Nail Him Yet (1964) 22 December 1964 (Season 1, Episode 11)
Bernard Archard
"Danger Man" I Can Only Offer You Sherry (1966)
20 January 1966 (Season 2, Episode 17)
Bernard Archard of course appeared later in Doctor Who: The Pyramids of Mars.