Can't receive external e-mail via Exchange

[skitrees]

This is the first time that I have used Exchange as my host for external
e-mail (domain). I have always simply hosted elsewhere and used the
connectors to bring the mail in to the domain.

The system I am attempting to setup right now is a Small Business Server
with IIS enabled, hosting a web site, and soon to be hosting e-mail.
However, I need to get Exchange up and running properly with external e-mail
PRIOR to changing the website's domain over to my server's IP.

So, here's what I have as it stands right now:
1 web site out in the real world being hosted by an ISP (this is also where
my mail is hosted at present)
2 Small Business Server with Exchange up and running internally, with the
above website on it for testing purposes - accessing it for testing via the
public IP of the machine - works perfectly.
3 Exchange on the above small business server, but exchange is only
services incoming / outgoing INTERNAL requests on the local domain and
servicing OUTGOING requests to the public, but I am unable to RECEIVE any
external e-mails sent to the IP (i.e. username@ip.add.ress.here).
Occassionally, it will flush and I'll suddenly receive all my tests, but it
has only flushed them through twice in four days. I receive no errors in my
event viewer logs, see nothing waiting in the badmail or queue folders. Is
there anywhere else I can find these e-mails?

Any help you could offer would be greatly appreciated. If you need
additional information, please don't hesitate to ask.

Synopsis: everything works perfectly except for the timely and consistent
receipt of EXTERNAL e-mails to Exchange.

Please remember that this is my first time using Exchange to host in this
configuration, so there might be some painfully obvious step I missed. If
so, please let me know.

Thanks!!

[skitrees]

Thanks for everyone's consideration. I found out that had I just gone live
and registered the DNS of my server - everything would have started working.

I simply had to add an @server.ip.address.here SMTP record in DNS, and BAM!
everything worked fine. I'll just get rid of this entry when I register my
IP with the registrars.

Thanks for all the great info in here though - some of the other posts ended
up hinting to this solution.

Thanks again,
Skitrees