Mac Mini not connecting to internet

Check in System preferences/network and check the IP address, network address, default gateway and DNS server are correct for the interface you are using to connect to the TC. Apart from the IP address the values should be the same as the MacBook Air if that works correctly.

The network address is probably not shown but the subset mask should be the same as the the Air and the default gateway is probably labeled as router.

You say the Air is connected to WiFi which I presume is your router were as the Mini is connected to the airport.

Does the Mini work if you select to connect to WiFi instead of Airport?

I am guessing on how your network is setup.

1. You have a router that connects to the internet and includes WiFi.

2. The TC connects by Ethernet to the Router and also provides a WifI signal labelled Airport.

3. Your TC is in Bridge mode for its network.

If this is not how you have it set up could you clarify.

The only thing I can think of without knowing exactly how your network is set up is to ask have you more than one DHCP server operating on the network. If you have and they giving out conflicting settings I could see that causing problems.

You can have two DHCP servers running but they must have their configuration carefully setup. On a home network it is not advisable to have more than one.

You can have two wifi networks as long as the wifi signals don't interfere with each other, I occasionally use two to extend the range of the network around my garden.

Where does the Seagate fit it this network?

Which device router or TC are you using for DHCP, also can you give the IP address of the router (internal address), TC, your Mini and the Air.

Don't post your external IP address, the internal IP are probably 192.168.x.x range, there are others but that range is very common for internal IP's.

Ok just seen the 10.0.0.x range, those are also internal IP.

Can you still post the IP addresses of the mini and Air.

I would only want one DHCP server for home networks unless you understand how to set it all up. Usually that would be the router. The router would give out the IP to clients, tell them to use itself in this case 10.0.0.1 as the Gateway to the internet (Apple label it router) and in many cases which DNS server to use, very often itself again but you could use others by setting them manually in Network settings on the Air and Mini.

If the TC is not set in Bridge mode it would be better to have it that way but read this article first.

Some information on when and when not to use bridge mode.

http://support.apple.com/kb/PH5104

Also the TC must have its own IP address, either choose one manually and set up the router not to give that IP address out with DHCP. Or easier still have the TC get its IP from the router like everything else.

Note the router is the DHCP server and the Air, Mini and TC would be DHCP clients, so you may see DHCP mentioned in the setup, be sure you know which is client and which is server.