AirPort Express no Internet connection

There is another possibility ..

Your Time Warner Modem is also a router.

You have therefore set the Express wrongly to dhcp and nat..

It cannot route because it is getting a 10.x.x.x address on the WAN.. which you cut off in the screenshot..

Because the DNS will be the modem itself in this scenario simply try putting the Express into bridge mode and power cycle both the time warner modem and the Express.

I thought what you do is to unplug it for 10 seconds

I have used the SB6121 with Time Warner's service, and it has always taken at least 5 minutes of power down time for the modem to reset. A few months ago after a power outage, I had to power off the modem for 30 minutes before it would completely reset and issue a new valid IP address.

Try power off the modem for 10 minutes. Longer is better if you can wait.

While the modem is powered off, perform a complete Factory Default Reset on the AirPort Express

Power off the Express for 5 minutes

Then, hold in the reset button first, and keep holding the reset button in for 8-10 seconds while you simultaneously plug the Express back into power

Release the reset button on the Express after the 8-10 second hold period and allow a full minute for it to restart to a slow, blinking amber light

Power off the Express

After the modem power down period, connect the Ethernet cable from the modem to the Express

Power up the modem and let it run for 5 minutes by itself.

Then, power up the Express and let it run a few minutes

Now use AirPort Utility to reconfigure the Express.

If things still do not work, you need to take the Express to an Apple Store to have them check over the device. If the Express works at the Apple Store, then there may be a compatibility issue with the modem and Express. I have had that issue as well in the past with both an SB6121 and SB6141 modem.

Two likely possibilities:

1) The modem has not been completely reset, so it will not release the IP address that was issued to your computer. That IP address that works with the computer will not work with the AirPort Express.

2) The WAN port on the AirPort Express has failed.

Suggest that you work on 1) first.....unless.....you have an Apple Store nearby to have the Express checked over.

What is the make and model number of your modem?

Please tell us what steps that you have performed to completely reset the modem.

Somehow during all the resets and connections when the computer was connected directly to the modem, the modem became

"associated" with your computer and ignored the requests from the AirPort for an IP address.

Only when you powered down the modem again for a more extended time did things reset correctly. Remember, the modem AND the equipment back at the cable company must both reset for a new connection to work correctly.

My AirPort is blinking amber and showing an error message that says there's no DNS servers

The AirPort Express would not be able to connect to the Internet if it was not receiving correct DNS information from the modem, so I have no idea what is going on here, and cannot duplicate the error to find a fix. You really should have the AirPort Express checked out at an Apple Store when you can.

In the meantime, the connection may heal itself overnight. Check the Express in the morning and report back.

Always remember that networking is one third science, one third luck, and one third voodoo, so things can be goofy at times.