You might not have been banned. Not being able to connect to the DNS or having it fail can be caused by a few things:
The DNS address serves couldn't be reached
The info on the DNS server couldn't be snagged from your ISP or the DHCP server
The DNS values in the dashboard are wrong.
I don't want to come off like I am insulting your intelligence, but check your internet connection to make sure you have the ability to connect. I'm sure it is all in proper order. So the next thing you need to do is check to see if you IP is set and passes all the tests. If it isn't then you can click the more link on the test page to follow the directions on how to fix it.
You may also want to check out if you are using a XBOX live compatible ISP. Click on Learn More to see if you are using the right ISP or to adjust your settings. You can also check out the connectivity wizard to find out if there are some other issues revolving around this.
Still running into problems!?!?!? try running the modem directly into your XBOX. This has helped me in a few time of need.
Here are some helpful links on what you can do when your DNS fails:http://xbox360help.blogspot.com/2007/03/dns-failed-on-xbox-360-live-test.html
And a link to a forum discussion regarding failed DNS