Scenario to consider:

If google handled your mails and all was fine until you transferred the www domain from “register” to
godaddy AND you were having your mails routed via some non-google entity BUT google was/is andling your mails then you may need to go to the godaddy console to avoid errors of the sort:

Technical details of permanent failure:
Google tried to deliver your message, but it was rejected by the recipient domain.
We recommend contacting the other email provider for further information about the cause of this error.
The error that the other server returned was: 550 550 sorry, mail to that recipient is not accepted (#5.7.1) (state 14).

MX records should point to googles own devices – not any other 3rd party. e.g. if they happen to include secureserver.net
then this should be edited out. As of writing the mx records should include.

MailServer Hostname:     Priority
ASPMX.L.GOOGLE.COM.     10
ALT1.ASPMX.L.GOOGLE.COM.     20
ALT2.ASPMX.L.GOOGLE.COM.     30
ASPMX2.GOOGLEMAIL.COM.     40
ASPMX3.GOOGLEMAIL.COM.     50
ASPMX4.GOOGLEMAIL.COM.     60
ASPMX5.GOOGLEMAIL.COM.     70

The CNAMES section needs

www @

mail gns.google.com

as a minimum and where ‘@’ by default points to the IP in your A Host section.

This is likely caused if, say, moving off gogrid where the records would have been changed to make the email work.
Once the relationship between the previous provider has been terminated, so may your routing!