Who can answer this without looking it up?
What was the first song (and whose song was it) performed by Elvis that got anybody in the music industry interested in him?

Blue Moon of Kentucky written by Bill Monroe

I remembered the song title, but had to look up (in my music files) the song writer's name because I couldn't remember it without a prompt. Does this count?

If I remember correctly, this song was what the movie staring Kirk Russell said about Elvis's beginning.

Dwight

Ummm, that's so close. Couldn't be closer. (That's a hint)

No the suggestion to answer without googling or checking sources was just a hunch I had that some Elvis fan would just know it. But anyone can answer.

On July 5, 1954, Presley began singing a blues song written by Arthur Crudup called "That's All Right". Phillips liked the resulting record and on July 19, 1954, he released it as a 78-rpm single backed with Presley's hopped-up version of Bill Monroe's bluegrass song "Blue Moon of Kentucky". Memphis radio station WHBQ began playing it two days later; the record became a local hit and Presley began a regular touring schedule hoping to expand his fame beyond Tennessee. (Wikipedia)

That's right, Moze. My version of the story is that when Phillips overheard Elvis jamming with the 'Starlight Ramblers', singing Crudup's song 'That's alright, mama', he's supposed to have said, "That's the sound I was looking for!" and released it, calling it 'That's All Right', with 'Blue Moon' on the flip side of the 78. I'm not a follower of early R&R music, but that's such a great story, I couln't resist posting.

Footnote:

In 1946 Arthur Crudup had taken the fourth verse from a 1926 recording, “Black Snake Moan,” by Blind Lemon Jefferson, a Texas bluesman, and country blues' first major star,

“That’s all right, mama
That’s all right for you
That’s all right, mama
Any way you do…”

and added some verses of his own.

Blind Lemon Jefferson