iTunes can't download song purchased from old computer, on to new computer I bought and downloaded a song in iTunes on a PC of mine. I never synced it to my iPhone. Well, I got a new computer, and no long have the old one. I think there might be a problem now.

Here is what happens when I click Check For Available Downloads in iTunes:


And here is what happens when I click on buy, for the song in the iTunes Store:


Is this a case of a badly worded dialog? I've seen something like this before in the App Store when I needed to reinstall a paid app. In that case I "bought" the app again, the second time without being charged.
In iTunes 10.3.3 or later, select Edit, Preferences, Store.  Under Automatic Downloads you can select which categories to automatically download.  If Music isn't an option, then you'll have to transfer your library manually.  I suspect Music is only an option in the US.

See iTues Store Support for more information.