I met a girl who sang the blues

Janis Joplin.

And I asked her for some happy news
But she just smiled and turned away

Janis died of an accidental heroin overdose on October 4, 1970.

I went down to the sacred store
Where I'd heard the music years before

There are two interpretations of this: The "sacred store" was Bill Graham's Fillmore West, one of the great rock and roll venues of all time. Alternatively, this refers to record stores, and their longtime (then discontinued) practice of allowing customers to preview records in the store. (What year did the Fillmore West close?)

It could also refer to record stores as "sacred" because this is where one goes to get "saved".

(See above lyric "Can music save your mortal soul?")

But the man there said the music wouldn't play

Perhaps he means that nobody is interested in hearing Buddy Holly et.al.'s music? Or, as above, the discontinuation of the in-store listening booths.

It's also possible that this line and the two before it refer to the closing of the Fillmore West in 19?? -- but I've been unable to verify that it was actually closed when this song was written.

And in the streets the children screamed

"Flower children" being beaten by police and National Guard troops; in particular, perhaps, the People's Park riots in Berkeley in 1969 and 1970.

The lovers cried and the poets dreamed

The trend towards psychedelic music in the 60's?

But not a word was spoken
The church bells all were broken

It could be that the broken bells are the dead musicians: neither can produce any more music.

And the three men I admire most
The Father Son and Holy Ghost

• Holly, The Big Bopper, and Valens -- or --
• Hank Williams, Presley and Holly -- or --
• JFK, Martin Luther King, and Bobby Kennedy -- or --
• or the Catholic aspects of the deity. McLean had attended several Catholic schools.

They caught the last train for the coast

Could be a reference to wacky California religions, or could just be a way of saying that they've left (or died -- western culture often uses "went west" as a synonym for dying). Or, perhaps this is a reference to the famous "God is Dead" headline in the New York Times.

David Cromwell has suggested that this is an oblique reference to a line in Procol Harum's "Whiter Shade of Pale", but I'm not sure I buy that; for one thing, all of McLean's musical references are to much older "roots" rock and roll songs; and secondly, I think it's more likely that this line shows up in both songs simply because it's a common cultural metaphor.

The day the music died

This tends to support the conjecture that the "three men" were Holly/Bopper/Valens, since this says that they left on the day the music died.

And they were singing...
Refrain (2x)