I assume you are trying to add a domain name manually from your Windows 2003 server IIS and all connections were already setup properly. All your clients can browse to your domain / IP but they were prompted for user name and password due to the permission was not setup properly.
Please follow steps below:
==================================
A) Create a web anonymous user
==================================
  1. Log into Server
  2. Right click on "My Computer" > "Manage"
  3. Expand the computer management console:
  4. Local > Local Users and Groups > Users
  5. Right Click on "User" > "New User ..."
  6. Enter a user name; example: domain.com_web
  7. Enter a password for domain.com_web
  8. Click "Create"
  9. Close this console
==================================
B) Assign Folder Permissions
==================================
  1. Right click on your web folders > "Properties"
    exp: C:domainsdomain.comwww
  2. Click on "security tab"
  3. Click on "Add"
  4. Select the "domain.com_web" user you have just created and "Add", click "ok"
  5. Allow permissions below:
    - Read & Execute
    - List Folder Contents (optional)
    - Read
  6. Click "Apply" and "Ok"
==================================
C) Add Virtual Directory / Domain in IIS
==================================
  1. Open IIS console
  2. Right Click on "Local" (Your server name) > New > web site > Next
  3. Enter Description = domain.com > Next
  4. Enter the IP address to use for this web site
  5. TCP Port = 80
  6. Host Header for this site = leave blank if this is dedicated IP, otherwise enter "www.domain.com" > Next
  7. Path = Your web folder path
  8. Exp: C:domainsdomain.comwww (The folder which we assign domain.com_web user to)
  9. Check "Allow Anonymous Access to this web site" > Next
  10. "Allow the following" = "Read" & "Run Scripts" > Next
  11. Finish
  12. Find the domain you have just added in IIS console and right click on the domain > Properties
  13. Click "Directory Security"
  14. Under "Anonymous Access & Security Control" click "Edit"
  15. Check "Anonymous Access" and click "Edit"
  16. Anonymous User > User Name = domain.com_web (the user you have created in section A above"
  17. Check "Allow IIS to control password
  18. Click "Ok"
  19. Under "Authenticated Access", check "Integrated Windows Authentication"