OK. I have made some headway on the issue. We found that 2 of the 15 mail servers we not accepting mail from us. We have made some changes to this and I was able to send a test message to email@example.com.
I sent this message as firstname.lastname@example.org
The message was received and replied to. We also noticed that it was only the eathlink.net addresses and not any of the earthlink.com or other companies that they have acquired. If you could test mail to the EarthLink accounts I would appreciate it.