Apple ID does not exist?

Contact Apple Support

• Apple ID (topic)
• [Other Apple ID Topics] button
• [Apple ID information is not recognized] button
• [Phone Call] button would be my choice

Alternately > Contact Apple for help with Apple ID account security - Apple Support

there is a contact link.

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. If you need to talk to them, ask them if they will do a Skype or FaceTime with you.

Apple Support using Twitter

Or fill out and submit this form.

You can discuss this with Apple support ay 1-800-MY-APPLE in the US. However, if the iforgot page does not recognize the Apple ID, there may not be much they can do for you.