That is some horribly mucked up thinking, not to mention cruel. ONE song? Can't be done. Even if I was only presented with one song, my brain would eventually be warping it into thousands. Not full fledged "professional" music, by any means, but my brain does tend to mess with the songs that get stuck in my head.
First and most obvious, if I get a song in my head that Weird Al Yankovic has gotten hold of, you can guaran-damn-tee that the lyrics will eventually be waffling back and forth from the original to the parody.
Second and not so obvious is my own brain's tendency to mess with lyrics. Especially if I only know part of them. I hate it when I've got a song in my head that I only know the chorus to. I'll either just have the chorus on endless loop or I'll find myself trying to come up with lyrics that scan and match the intent. The latter is not a good thing when I'm driving. Fortunately, I've got a working radio/cd player in the car to keep that from happening.
And lastly is my brain's tendency to do mash-ups if I'm stuck with an internal song for too long. I've even got a couple that would probably work really well, if I had the talent and tools to muck about in mash-up land. (I still say that "Rubber Ducky" and "Notorious" would work. Trust me, I'm a MBLF.)
I did answer the question, by the way. "I Wanna Be Sedated" by The Ramones. Because, you see, this is the reset song that I use. If I've got something stuck in my head, I can start singing this and it will go away. And then I can easily replace this with any song that I so choose. It's always nice to have a reset song.