Is your lan and the lan at the other office using private IP's? Like through a VPN or something else. Can you ping the router at the other office? If you can, then can you ping the private IP of the web server? If you can, just go into your host file (etc/hosts) and add a line for it showing the private IP as the address. Entry would be something like:
www.yourdomain.com 111.222.333.444 (substitute private IP for the numbers)
When you have a default gateway to get out to the internet, and your server has a public IP and it will of course have the private IP, your gateway doesn't know what gto do with it. So if you edit your hosts file to reflect the private IP it should work just fine (assuning of course that you can ping the IP from your office). If not, then you have to resolve the router issue as well. Take a look at these things and then repost.