Don't setup TC by wireless .. it just is too hard.. although the Airport utility in iOS may work better.
Plug in by ethernet.. bridge the TC and plug in to the router by ethernet.. I am hoping that is available.. if not tell us, but we recommend not using the join wireless network.
You can always use the TC by ethernet even as you have internet via wireless. but you connect use wireless to both unless the TC is setup for connection correctly.
I have not tried this with the latest airport utility... and if you are such an unfortunate to have ML only for setting up then no wonder you are in trouble.
Press and hold the reset on the TC.. you wait until the front led flashes rapidly.
In the network preference.. again my experience so far only up to SL.
Set a fixed IP address for ethernet.. 10.0.1.10 would be a good value.. subnet standard 255.255.255.0 .. no router (gateway) no dns address. .that will just mess things up.
In the order list of priority for connection.. ensure wireless is at the top.
Do not even bother opening airport utility..
Just open finder and it should find the TC.. if not use go, go to server.. afp://10.0.1.1 and see if it pops up.
FYI: I called Apple Support and they said that without a hardwire connection from the Time Capsule to the Internet Modem the system will not work. They said it might be possible to connect the TC for use strictly as a backup drive but that they do not support that at Apple Support. So, I will search this support forum and, if I don't find what I need, will start another thread. Again, thanks for your help.
I think.. you will get nowhere fast using v6 utility.. you must use the older utility.. 5.6.
Apple have so dumbed down v6 as to make it useless.
There are plenty of posts about how to install 5.6 under ML. I don't think it is that hard.
Download the 5.6 dmg.. open the pkg.. then extract the files from the pkg.
There is a free utility to do this.. as well as shareware Pacifist.
Simply load the files manually and then run it..
I am about to try it myself but confess it has not yet happened.
Make sure the TC is different IP range to the main router..
Set static IP in the computer and it must work. By all the TCP/IP I have ever learned it has to be available to the computer.. but I will test myself.
I had updated my wireless modem from a 3g USB device to the Jetpack 4g some because of a free upgrade time ago. I have been traveling a lot and not had my TC connected. In the mean time I had bought a new 2T TC. I didn't realize that the TC needed a direct ethernet connection to the iMac so when I connected it and it didn't work, I was confused. Thanks to your advice (above) I have reverted to the 3g USB device and am now up and running both on the Internet and the TC backup drive. Thanks again.