Hello s_hallfurman,
Welcome to Apple Support Communities. You will need to regain access to the old Apple ID in order to delete it. In order to do so, you will need to reset the Apple ID password. Follow the steps here to do so: If you forgot your Apple ID password
Reset your Apple ID password on the web
If you don't have a trusted device, you can reset your password on the web — but the process might take a little longer.
When possible, the web process redirects you to a trusted device. If you'll have access to one of your trusted devices soon, it might be faster and easier to reset your password then.
Reset your password at iforgot.apple.com
Once you have access to the account, the guidance needed is found in this Apple Support article: How to delete your Apple ID account
How to permanently delete your Apple ID
Sign in with your Apple ID at privacy.apple.com on a Mac, PC, iPhone, or iPad, and select “Request to delete your account”.
When you request account deletion, you'll receive a unique alphanumeric access code. Make sure that you keep this access code in a safe place. For a short period of time while your request is being processed, you can contact Apple Support, provide your access code, and we’ll help you cancel your request so you can resume using your Apple ID.
Be sure to read the steps prior to deleting the Apple ID, and let us know if you have any questions.
We hope this helps you.