You need a MX record created with the IP address of your router. Depending on if it is statically configured or DHCP assigned, will make the configuration steps a little different. First if you don't already have one setup an account with a DNS service provider. I use
www.dyndns.org to host my domain name and it is free (but donations are encouraged) and there are two different services: DynamicDNS or StaticDNS. Once you create that account and the information propogates around the Internet you should be able to send and receive email. Also make sure you remove any SMTP settings that point to the earthlink SMTP servers. Your Exchange server should have a default gateway and DNS settings configured so it can communicate with other SMTP servers on the Internet for email transfers. Your router should have a port redirection for port 25 pointed to your exchange server as well. Ultimately what should happen is when you send an email, your Exchange server will lookup the IP address (via their MX record) of the domain you are sending the email to so that it can establish a connection to the receiving SMTP server and transfer the email message. The same would work in reverse when other send you an email, that is why you need a MX record for your domain.