There are three separate things to look at here.
The first (DNS resolution for www on the local intranet) is well-covered by another answer, with the addition that if you host your own web site at the same location as all of your domain users, you'll want to use the internal ip address rather than the public ip address.
The second is the Windows 7 vs Windows XP issue. Here, you want to look in DNS settings for your network adapters. I'm not sure what your network setup is like, so I'll just give you a generic idea of what the screen looks like (below). The main thing is that it's likely your Windows XP machines have something a little different here than your Windows 7 machines. You're looking at the options in the middle of this Window:
Finally, you may want to also support allowing your users to enter
example.org in addition to
www.example.org to reach your web site. You can do this, but to make it happen you have to run iis on your domain controller. There are some good reasons you may not want to do that. But if you decide to go head, you just need to set the default page for iis on your domain controller do a permanent redirect to the actual (www) web server.