Cannot Load Web Page Unless DNS is changed to Public

Hello,

Recently one of our clients vendors updated their webpage, and as a result, all clients of theirs would need to upgrade their browser to IE9 or use Google Chrome. Our client is on Server 2003, which only allows us to run up to IE8, so Chrome was our only option. What were seeing was that mostly text was resolving on the webpage, and things were not fully functional. We went though various troubleshooting steps to resolve this: reset settings to default, clear cache, flushdns, compatibility mode. All of it, no dice. So we went out on a limp and made public DNS primary and local secondary. This fixed the issue with the website, so we made the change to DHCP, and went on our way. The next day, our client reported slow log in times, and multiple SQL applications were not functioning normally. We changed the local DNS back to primary, and public back to secondary and those problems disappeared. Of course, as a result of that, the website cannot be accessed within the network. Does any one have any idea what the issue might be or how to fix it, or is our only real option to upgrade the server. Thanks!