Apple ID out of service

See -> Having trouble signing in?

https://iforgot.apple.com/password/verify/appleid

If you've forgotten your Apple ID email address or phone number

If you've forgotten your Apple ID email address or phone number – Apple Support (UK)

See -> If you can't connect or sign in to iCloud

If you can't connect or sign in to iCloud - Apple Support

What do you mean "out of service" exactly?

Are you getting an error? If so what does it say?

Does it say its "disabled in the App Store and iTunes"? If so, see here; link-> If a message says 'Your account has been disabled in the App Store and iTunes' - Apple Support

Does it say its 'Disabled for security reasons"? If so, see here: link-> If your Apple ID is locked or disabled - Apple Support

Does it say something else? If so what does it say exactly?