The story of Big Star had all the elements of a great rock ‘n’ roll story, except anyone paying attention to it.

The Memphis band made three critically-beloved power-pop albums in the 1970s whose impact rippled through generations of musicians and music fans to come. Big Star had a charismatic, enigmatic frontman in Alex Chilton, already a pop star for penning and singing The Box Tops’ “The Letter.” And they had a bonafide rock and roll tragedy in the story of Chris Bell, the McCartney to Chilton’s Lennon, who died in a car crash when he was only 27.

The only trouble was that Big Star couldn’t sell any records, and much of the world remained totally oblivious to such great music and a great story. The band disbanded in the mid-1970s, but true believers from the Replacements to Elliott Smith kept the flame alive. For younger listeners, Big Star was a band you found through your favorite bands.

Now comes “Big Star: Nothing Can Hurt Me,” a definitive documentary to tell Big Star’s story and make sure their place in rock ‘n’ roll history is properly secured. Writer-director Drew DeNicola takes the viewer through the creation of the band and its three albums, “#1 Record,” “Radio City” and “Third/Sister Lovers,” talking to surviving band members, Memphis musicians and producers, critics and family members.

Two emotions fight for dominance while watching the saga — the exhilaration that comes from seeing great artists working at the peak of their powers, and the frustration of watching the world ignore those great artists. Theories abound as to why Big Star never stuck — they were bringing fragile, tuneful pop music into an early ’70s music business defined by arena shows and big, bombastic sounds. Bad luck also played a role, as the major-label merger that looked like it would rescue Big Star ended up torpedoing its chances.

After the band broke up, Bell and Chilton seemed to go in opposite directions. Bell continued to toil and perfect the Big Star sound (if nothing else, the film will ensure Big Star fans scoop up Bell’s excellent solo work), while Chilton seemed to repudiate its ear-friendly sound, defiantly making dissonant music with bands like Panther Burns. Eventually, Chilton resurrected Big Star in the 1990s, so he must have somehow reconciled his connection with the band.

A recurring visual motif in “Nothing Can Hurt Me” is the camera panning over shelves and shelves of old Big Star recordings, tapes all carefully labeled in black Magic Marker. It could be something out of a museum. But the genius of Big Star, and of “Nothing Can Hurt Me,” is that when you take those recordings off the shelf and cue them up, the music sounds as potent and as relevant as anything out there.