I tunes Music authority issue

My new Lenovo Laptop is authorized for iTunes and i have my apple username which includes my @gmail account and my original I Tunes Password.

I have a number of purchased (i.e. paid) I tunes songs. All played routinely on my old laptop which for several years has my @gmail included in my username.

Now when I select some of those purchased songs I get an error message " do you wish to authorize this song for tis pc ? you purchased this dong using xxx@slingshot.co.nz and asks me for a password..

I have tried replacing the @slingshot.co.nz with @gmail.com and my iTunes password. -failure.
I then leave the @ slingshot line as is and enter the original iTunes password I had when I used slingshot-failure.

I then select "forgot user id password" then get a text with an authorization code-apply it but then just get "this pc is authorized" and quoting my @gmail username.

I registered with iTunes forum but ability to enter a detailed question is severely restricted.

Any ideas why on some of my purchased songs I gr confronted with this issue?

Help please.

Only a guess, but you may have to Authorize itunes / the computer under the original slingshot account. Looking at the songs purchased here they are all from my old paradise account (which no longer exists), if I try to use one of my other current accounts it wont play.

The only problem with old accounts is you may not have access to them any more if needed so you have to change the recovery options once in.

Don't know if this will be of any help https://support.apple.com/en-us/HT203160

Thanks, Wainui I have copied the link you supplied into MS Word so that I can try the various options
Neil