Interesting Activation Lock Conundrum...

What if since you registered the device you have changed the email associated with your apple account

so the ''apple ID and password that were used to set up this iPhone'' no longer exists

To Apple's system this is still the same Apple ID. Any password changes should be recognized by the system now.

If you know the password and have changed the email address, you should be able to turn off activation lock via the website option.

Doing this you can enter any email address you wish along with the current password, disable Find My Phone and remove the activation lock.

This implies your don't have the phone, but the directions are appropriate for your scenario.

https://support.apple.com/en-ca/HT201441

.

If you are the original owner, take the device, the original purchase receipt with the serial number, and a photo ID to the nearest Apple Store.

Genius Bar Reservation US

or contact Apple ID Support. They will need to see the original purchase receipt/paperwork also.

Apple ID Support

Apple ID Support (2) 

Apple Support by e-mail or chat         Select your device, Battery, Power and Charging, then Power adapter not working to get a chat option. 

Apple Support using Twitter

Or fill out and submit this form.