how to access old apple id that no longer exists?

I once had an apple id using an email address I no longer use. This was from years ago, before I had iPhones, before app stores, from the days when there was only iTunes. Years ago when I moved, I transferred all my CDs to iTunes. All that music is apparently associated with that old apple id. When I got an iPhone, 7-8 years ago, I got another apple ID, using an email I still use today. At some point I'm pretty sure I "merged" those two apple IDs. However, now when I try to play any songs from albums I purchased as CDs years ago and added to iTunes, I'm told I need to associate my current computer with the old apple ID I had when the music was added to my iTunes library. I tried doing this, but I can't remember the password for the old apple ID, sO I tried clicking "change password" (Note: I can now access the email address for that old apple ID if I need to, but that is not the problem. When I start the "change password" steps, I get an error saying the apple id, the old one that iTunes is asking me to authorize the computer to use, does not exist! How is it iTunes can ask me to authorize a computer to access music "purchased" with an apple ID that DOES NOT EXIST? And how am I supposed to authorize it? Thanks.

NOTE: I am using a Mac Mini 2014, but that option wasn't included in the list of devices. At the time I added the music to iTunes, I was using a 2008 MacBook Pro