I purchased a song but when it downloaded it was not the full song

Try contacting Apple with Express Lane.

Let them know what happened and they should should be able to help ya out.

if the song cuts off early try deleting it out of your library then going to the new "Purchased" feature and redownloading (its free). I had to do this with some of my tracks that didn't fully download (though they said they did). Once I redownloaded I had the entire song no problem.

Make sure you delete the file completly from computer...that way iTunes will see that it is not already downloaded and will allow you to download it again.

in your itunes menu (top tool bar) go to "Store" then scroll down and you should see an option that says "Authorize this computer"