It doesn't matter about the old hardware. Just sign in with your account information.
Click on this link to read what to do "If you forgot your Apple ID" --> https://support.apple.com/HT201354 Note that typically this is an email address you use.
Click on this link to read what to do "If you forgot your Apple ID password" --> https://support.apple.com/HT201487
or go directly to this link --> http://iforgot.apple.com/
Also read about "What to do after [or before] you change your Apple ID email address or password" - https://support.apple.com/HT204071
If you still need help:
Contact Apple for help with Apple ID account security "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues." Click here --> https://support.apple.com/HT204169