Help Needed - iTunes & Authorization

I had to do a clean reinstall of my MAC OS, after restoring my iTunes library from Time Machine all the songs and apps are back but I cannot play any of my purchased songs or apps. iTunes keep on asking that I need to authorize the computer - which I have done using my Apple ID. When I play the song up comes the message box asking for Authorization I then do it and get a confirmation message box saying I'm already Authorized BUT I still cannot play the songs!

I've contacted iTunes support and read all the Apple iTunes help and how-to's and they just say De-authorize and then Re-authorize as a Admin o the local computer (this I have all done). Apple support seems to be lost as I'm now being referred between different support numbers?

Has anyone seen this or has any idea how to fix?

I tried that but cannot find the folder SC Info under any of the Users or Shred folders? This is a new installation but I searched the whole drive and nothing.

I did notice today that all my songs where purchased under my Account Name as Xxxxxx but my Apple ID is actually Xxxxxx@gmail.com, the names are the same but the @gmail.com bits are missing. Then I went on to the itunes store and purchased the free song for the day and this song played 100% and Get Info showed my Account Name as Xxxxxx@gmail.com where all my existing songs are only Xxxxxx. My AppleID has not changed but seems there is a different way in assigning my Account Name, can this be the problem and how to fix it?