Can't see website from laptop when connected to a different LAN

I have a Windows 2003 server acting as a web server for a website that
I'm hosting. I have several Windows XP boxes on the same LAN as the
web server. One of those boxes is a laptop running Windows XP. When
I am connected to the LAN with my laptop, I can access the website
just fine by using the domain name I registered.

I can also hit the website through the domain name with any of the
other boxes on the LAN as well as any box that is in an outside
location and not on that LAN. However, the laptop that is on the LAN
does not see the site when disconnected from the LAN and plugged into
another LAN elsewhere. I have internet access on my laptop through
the off-site LAN. I can also ping the webserver without a problem
from the laptop while connected to the off-site LAN.

But when I try to access the website from there, I get prompted for a
username and password - as if I was trying to map a drive from the
server. No matter what I enter into the login screen, the web browser
then gives me an HTTP 500 (Page cannot be displayed).

I'm guessing this is some kind of networking issue with my laptop
running on a different LAN. Any help would be greatly appreciated!