I'd suggest that you try a local configuration and make sure you have allowed for management of your server over the private network. As I've never had this problem out of the box, I can only guess at checking some of the following:
Since DHCP appears to be working, check if you can browse to ANYTHING. It is possible that you have your NICs confused and have programmed the wrong side to local. Simply swap the cables rather than try to reconfigures. If you decide that you need the NICs as is for performance reasons (I have a DSL line with a 10 MB card and 10/100 on the internal LAN), you can reprogram AFTER seeing if this fixes the problems.
Try browsing to the server by simply typing the IP address of the internal NIC. Make sure you are actually being provided web services. If you have decided that this server is NOT a gateway, the browser will most likely not be loaded (I haven't tried this, so I'm guessing, but it does make sense to no load the http daemon if you're not providing internet access on the server).
The management control panel doesn't require anything different than the web browser. Your local network configuration (MyWorkgroup vs. YourWorkgroup) shouldn't interfere with the ability to browse your server.
If your client has both dial-up and LAN connections, make certain that the connection tab is set to dial when a local connection is not available. If always dial is set, you'll never get out on the browser.
The last suggestion is to (at least temporarily) disable any personal firewall software on the workstation. Although not probable, it is possible that the software is improperly configured, precenting access.