Check the MX (and associated A) record for the public IP address for inbound delivery. Also check to make sure Exchange services are running. If outgoing mails are not working and you changed connection properties, be sure the edge firewall is configured to permit outbound SMTP (port 25) connections. You should provide more details about any specific error messages or changes that were made.
There is no “Edge” server with exchange 2003. Do you send directly to the internet or do you use a smarthost server through your ISP? You MUST have a static IP in order to register MX records. MX records will not change if your IP changes. So start there.