Q: Apple ID linked to two different e-mail accounts

When I moved country I had to close out an e-mail account from a local telcoms supplier.  I changed the e-mail linked to my AppleID.  Things were fine for several years, but with recent upgrades to iTunes I now find that I cannot play certain songs.  When I check File/Info they show the correct AppleID name but the old e-mail.  I get asked to authorise the computer under this AppleID, which I can still do, even with the old e-mail as I still know the password.  But I still can't play the song.  Also, when I log into the AppleID using the old e-mail it does not show the purchased songs.  So why does File/Info show this AppleID if the song is not listed as purchased?