There is a way to do this.. but as Bob noted it was not how the TC was designed to work.
1. You need to swap control of the airport utility from wireless to ethernet.. here.
2. When I swap to ethernet all my other airports disappear.. and only the TC plugged in by ethernet is available.
3. Normally I recommend a router setup but static also works.
Click on the TC to bring up the summary.. click on the edit.. (hidden by the floating help details about the error.)
4. Go to the Internet tab. I am using the default IP of the TC.
This is based on your main router using a 192.168.x.x address.
Fill it out exactly as follows except your DNS will be same as your wireless main router IP eg often 192.168.1.1
Or use 8.8.8.8 .. doesn't matter as it is not used. Also click on Internet Options and select Link-Local only for IPv6. This is important now.
5. Go to the Network tab and fill out a suitable IP range. Use DHCP.. no NAT. Then click update.
6. Click on the wireless tab and select off for wireless.. you really don't want or need it running.
7. Fix the error/s
Click on ethernet unplugged.. this is your wan port on the TC.. Just ignore it and then you get a green light.
Now it is important to note if you have other airports they will not show up as long as you have airport utility selected to ethernet.
8. Fix it in the computer.
You need to reset the order to make sure wifi is the top of the list.. ethernet cannot be the top as it has no internet connection. Both should be green and showing connected.
Now check in Finder and you should be able to access the TC.. and check your browser to make sure you have internet connection.
Please note .. in the end a USB drive.. nice small self powered drive is faster, simpler, cheaper and more reliable with Time Machine than doing all this.
