Hello xsamx87b,
It sounds like you are having some trouble playing purchased music from your iTunes library on your PC. There's an attached link with troubleshooting steps that may relate to your concern, which is If iTunes for Windows prompts you to authorize your computer when you try to play purchases. Were you able to complete any steps from this?
Just in case the Apple ID was different when the content was purchased, double check to determine the Apple ID originally used.
Use Edit > Song Info (iTunes) or Song > Info (Music) on the file, then File tab, and look for 'Protected AAC' or 'AAC'. Let us know what you see there. You can also check if the song(s) appear when you See your purchase history for the App Store, iTunes Store, and more. If it doesn't, this means there has to be a different account involved.
As a test, we can move and delete one song, empty the recycle bin, then try to play the song, which will prompt an alert to locate the file once more. Instead of trying to find it, click cancel in order to have the streaming feature locate the necessary files. This process is further explained here:
If a customer sees an exclamation point next to their items in iTunes
Before we continue into further detail, we'd like to hear the outcome of the above.
Enjoy the rest of your week!