Internet connection not recognized with Airport Express

Question

Prior to getting my first Airport Express, I'd had my broadband modem connected directly to my Mac mini. Since I hadn't an iphone or ipad back then, wireless access wasn't an issue. When that changed, I purchased a first-generation Airport Express. My setup was as simple as it gets:
a) Unplug the ethernet cable from my mini.
b) Plug the ethernet cable into the (single) ethernet port on AE.
c) Using Airport Utility, create a wireless network.
d) Join that network with each of my devices - mini, iphone & ipad - so I might access the Internet wirelessly.
That's it. I've no printer or sound system to which I need wireless access. No extended wireless or other complicated networks.
My hardware setup needs haven't changed. However, because I was having intermittent problems with the wireless connection to my mini, I thought the new AE with its dual bands might help. I bought one yesterday, thinking to use it in place of the old AE.
I figured the setup would go as easily as it did last time. I was wrong. I've spent the last six hours trying to get the new AE to work. The problem is that the Internet connection is not being recognized. First, there was a message about a "self assigned IP address." I googled that, found discussions here about it, and (seemingly) managed to get rid of that problem. But now, no matter how many times I've unplugged/factory reset/restarted the various devices (AE, modem, mini), I can't get an Internet connection. The only way I've been able to write this message is to have reconnected the broadband modem directly to my mini. So I am completely without wireless at this point.
What is wrong? How the heck can I fix this?

Answer 1

Well, thanks to my own stubborn tenacity, I finally got my spanking new Airport Express to work. I'd tried several factory resets, following the recommendation that one power down all devices (not just the AE), plus other fiddling about, all to no effect.
The last factory reset I did differently. I kept my broadband modem and computer still on, and only unplugged the AE then plugged it in again while depressing the reset button for ten seconds. (Those factory resets aren't easy to do when you've only two hands!)
Finally, this time when I clicked the wi-fi icon in the menu bar, I saw the AE listed there, which allowed me to follow the setup process as described here.