I have been an Adobe user for decades. Over the last 10 years, however, I have only used Adobe products provided on my university's computer. Having recently retired, I now wish to use Lightroom, which I first bought during version 1.4, or maybe v.2.
I do not have a record of my old Adobe ID nor do I have my old Lightroom serial number.
How can I begin to retrieve my credentials and be able to use Lightroom again?
Dont' go down this rabbit hole. LR 1 and 2 are outdated, unsupported and downloads probably don't exist anymore. Even if you lay your hands on an installer, unless you own a very, very old computer and operating system that's compatible with really old software, this is a fruitless pursuit.
Create a new account and spend $10/month for a Creative Cloud Photography Plan. Trust me, you'll enjoy your retirement a lot more with modern software that's compatible with modern devices. And you get free upgrades for as long as you remain a Creative Cloud plan member.