Configured Airport as Bridge and use OS X Server for DHCP and DNS, no Internet I want to use my Mac Mini as an OS X Server with the following services: 


DNS
DHCP  
Open Directory
Profile Manager


I configured my Airport Extreme under the "Internet" tab to use my static IP supplied from my ISP. I'm using the IP of my Mac Mini as the primary DNS server and no secondary DNS server. Under "Network", I have router mode set to Off (Bridge Mode). 

When I open Safari on the Mac Mini server, I'm not getting any Internet connection at all. I checked in the DNS settings of the server and made sure I had forwarding servers pointing to my ISP DNS and Google DNS (as backup). Under Sys Prefs, I have a static IP assigned and pointing DNS to itself.

How can I have my Mac Mini supply DNS, DHCP, and RADIUS wireless support and still get Internet?
You're trying to accomplish more in one step than you can handle. Break down your problem into subproblems, and solve each one.

The first you want to get working is to have an internet connection on your Mac Mini when the Airport is set in bridge mode. Do this without setting up DNS-servers and changing DNS settings to use your Mac Mini as the DNS server.

When you have working, you can add on the DNS.

Basically at this point you want to ensure:

a) That the Mac Mini's network port is setup with the correct IP, subnet mask and default gateway. This is the static IP and network settings, you have been supplied by your ISP.

b) That your Mac Mini can "ping" addresses on the internet. Open Network Utility and try to an address on the Internet. Try first with an IP (such as 23.78.125.15) and then with a DNS-name (such as www.apple.com).

Remember that in this (simple) scenario, you can only use an IP-address once. I.e. if you assign a static IP to the AirPort Extreme, you cannot assign the same static IP to your Mac Mini.

If you have got only one static IP, you cannot use that IP on both the Airport Extreme and on your Mac Mini.