OK, first the background information.

The state network assigned me 2 public IPs which are NATed to 2 private IPs. The private IPs are 10.16.50.100 and 10.16.50.102. The state network forwards all traffic going to the 2 public IPs to those 2 internal IPs, so any device on one of those internal IPs will be visible by both the external and internal IPs, even though the NIC will only be assigned a single IP.

Now, I have had a Slackware 9.0 server setup as my Web and DHCP server. It is setup on 10.16.50.102, and worked fine for the last few months. People on the internet and the LAN could see the website without any problems.

Slackware 10 was just released, and I wanted to redo the server anyway, so today I started with a fresh install of Slackware 10 on a different machine. I then installed all the programs that where running on the Slackware 9 machine, and then their configuration files.

To clients on the LAN, the two machines are identical. The problem arises on the internet. When I bring down the Slackware 9 server, and bring up the Slackware 10 server on 10.16.50.102, the Slackware 10 server does not accept any traffic coming from the public IP. Internal traffic still works perfectly, however. I take the 10 server down, and put the 9 back up, and our website is instantly available on the public IP again.

So what is the problem? These 2 servers should be completely identical. Is there something that needs to be setup differently on Slackware 10 to allow connections from the internet? There is no firewall on the machine.

Can anyone give me an idea as to what the problem might be?

It sounds like the default route is probably wrong on the new server. Are the routing tables the same on both machines?
route -n

The line beginning "0.0.0.0" is the important one in this case.

The routing tables match on the two servers.

Can you see any traffic coming to Slackware 10 on the 50.102 interface?

If not, it is possible the state network has bound the mappings to your Slackware 9 NIC's MAC address.. guessing.

What error are you getting? Connection refused?

Can the slack 10 server see the internet ok? - ie:
lynx http://www.google.com