I'm still confused
Do you actually need the font because you're making changes to an existing design?
Or do you just need the font because Adobe is defaulting and substituting a font because the font is missing?
Two different issues.
If you only need to open that previously created file on your new system, go back to your old computer, open the file and convert the font to curves.
Save the converted file with a different name so you don't lose that original file ......just in case you find the font one of these days.
Now open that new file that you converted to curves and Adobe won't default and substitute the font on you
You can also place the file in (instead of opening it) Illy.
Flatten and you should have the file/font intact
But, if you actually need that font because you need it to make changes to your original design, then you're probably gonna' have to find it on that old computer.
It's there someplace.
Put on your Columbo jacket and start looking......
If nothing else, you could always post a visual, chances are one of our font gurus will be able to identify it for you and maybe you can then grab a whole new font file, download and install it somewhere where it won't get "lost"
Thumbs up for the Font Management suggestion
I couldn't work without one
Diane