iTunes says computer not authorized. When I try to authorize computer it says it is already authorized but will not play song

I'm experiencing the same thing under iTunes 11.1.1:

1. iTunes says the computer is not authorized, prompts me to authorize
2. I enter my credentials, iTunes says computer is already authorized
3. When I attempt to play song, iTunes starts at bullet point 1 above over again.

My attempted fixes:

1. I tried everything in this support document, to no avail: http://support.apple.com/kb/TS1389 (Note: I cannot find a SC Info folder on my Mac)
2. Deauthorize and then reauthorize computer
3. Delete song and try to redownload from iTunes store - there's only a button that says 'purchased' with no option to redownload it

Note: I am using only one iTunes account, and I double checked the song info - I'm authorizing the correct account - 12 songs from the same album purchased at the same time play fine. As does the song in question - from the finder. Only iTunes stubbornly refuses to play it.

The most odd thing is that iTunes music is DRM free - the song in question was purchased only a few months ago. Thus there's no need to authorize the computer to play it.

I was hoping that iTunes 11.1.1 would cure it - no dice.