How do I authorize my computer through Apple iTunes?

My problem is, I click on a song I bought in the iTunes store and it says my computer is not authorized. So I enter my apple id and password and click authorize. It then says this computer is already authorized. So I click on the content I want to play, and it happens all over again! So how do I get out of this loop to play my music? Thanks for any help or suggestions! I actually have deauthorized it and reauthorized it a few times on both computers I am having this problem with. I have also uninstalled and reinstalled iTunes on both computers, too. Thanks for the suggestions though!

1) try to deauthorize it and reauthorize it maybe that'll work, or redownload itunes.

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