Just off the top of my head:
In order for you to setup your exchange server for internal and external email you have to do a few things:
1. You need to allow the appropriate ports for incoming and outgoing email on the ISA server (POP-110, IMAP-143, SMTP-25, etc.). You probably want to use a server publishing rule on ISA for exchange. Be sure to read the articles to cover yourself (Security, Best Practice).
2. You need a MX record on the Internet for your domain name. The ISA server needs to be able to resolve this hostname internally. Also, if you publish your server through ISA, the hostname should resolve to an IP on ISA.
3. IF exchange and ISA are on the same server, you probably have run across a port conflict with ISA and IIS. There are articles on this.
4. For external access to OWA, I would recommend you use SSL. There are stronger authentication mechanisms out there as well, such as SecurID.
5. Make sure your exchange server can resolve the destination domain name (DNS). This will require external resolution. Follow best practice.
Best bet is to read some of the articles on Microsoft. The configuration is not that complex.
P.S. I hope domain server doesn’t mean domain controller. If so, you should go to great lengths to ensure security is implemented correctly.