*Winter Soldier Spoilers* When Zola is showing the clip video of how Hydra has secretly been shaping the world over the years, a newspaper clipping of Howard Stark's death is briefly shown, alongside photos of the Winter Soldier. It was pretty obvious then that Hydra had him assassinated, most likely via the Winter Soldier; it was easy enough to infer that I went in to Civil War knowing that would be a major plot point. If Cap didn't himself didn't figure it out then, he would have shortly thereafter, likely before the events of AoU.
Not saying that I agree with or defend the rationale here as to why he couldn't lift the hammer, but Cap knew about the event in question by that point.
Just rewatched that scene, and am reminded how amazing winter soldier really was. Great movie. Also yeah it totally could have been implied that winter soldier was responsible for the starks' accident even then. So I like this explanation. ---