YUCK !!!
Inside the Exchange System Manager, expand the 'Servers' icon, expand the icon for the server you are using, expand 'Protocols', expand the SMTP icon, right-click the queue you are using, left-click properties, click on the 'Access' tab, click the 'Relay' button. (I hope I remembered everything)
What do you have selected here?
I have added my private network address here. It allows only those systems with our private network address to send/relay e-mail.