In the Guy Pearce version of The Time Machine, he can frustratingly appear to have managed to change the past, but since he built the machine because his fiancé died, no matter what he does, she dies by various means: he can change the past but not the essential aspect that she indeed always dies. (It seems to me that there are other outcomes that would make him create a time machine -- what if she were merely extremely traumatized? Or merely insisted that he build the machine so she can see it, but in this movie, The Mind of the Creator (or whatever) keeps coming up with no plot lines that do not end in her death.
Anyway, I think the Pearce version may have been the first time travel movie that showed how the past could not be essentially changed. Of course in, for example, A Christmas Carol, the Ghost of x-mas past tells Scrooge that he is seeing shadows of the past that simply cannot be changed. But that is different than my question: a changeable past, but not changeable in the desired way.
One minor thought: I recall the line from "The Island of Dr. Moreau" in which the good doctor expresses frustration with his results: "The damned beast flesh keeps growing back!" and this strikes me as eerily similar to what happens to the professor in Pearce version.(I am pretty sure the originally Wells story does not have this essential immutability theme in it.)
EDIT: It appears there were many stories before 2002 The Time Machine which (I am guessing based on the responses) had the details of the past change but not the main outcome so changing to first movie.