A bit more information like what version of AirPort Utility you are using might help us narrow down the possibilites.
If you are not sure what version you have, click the AirPort Utility menu at the upper left corner of the screen, and then click About AirPort Utility. Post back with the Version number that you see there.
Your post did not mention any troubleshooting steps that you may have already performed, but we assume that you have completely power cycled the entire network in sequence a time or two. Would that be correct?
I was having the same issue trying to setup the 5th gen airport extreme. I had the airport utility v6.3 on the iMac. I could connect using the wifi but my airport utility could not find it and gave me an error message. I too had the amber flashing light. I took an old white macbook running airport utility v5.6 and was able to set the airport extreme up. I still can not get my airport utility v6.3 to find the extreme. I'm sure there is a software update to fix this. Until you can find it, you migh try using an older version of the airport utility software............
On the older version of the AE you can still use older airport utility.
But once you load the new one you cannot easily go back.. you can load an older 5.6 version though.. instructions below.
For 6.3 you need to run ipv6 local link.
How to load 5.6 into ML.
1. Download 5.6 for Lion.
Click to open the dmg but do not attempt to install the pkg.. it won't work anyway.
Leave the package open on the desktop so you can see the file. AirportUtility56.pkg
2. Download and install unpkg.
Run unpkg on the desktop.. If your Mac refuses to run the software, because it wasn’t downloaded from the Apple store, go to security in preferences and allow other software to work.. this is limitation of trade methinks. You can set back later if you like.
Now drag the AirPortUtility56.pkg file over to unpkg.. and it will create a new directory of the same name on the desktop.. in finder, open the new directory, drill down.. applications, utilities .. there lo and behold is Airport utility 5.6 .. drag it to your main utilities directory or just run it from current location.
You cannot uninstall version 6 (now 6.3 if you updated) so don't try.. and you cannot or should not run them both at the same time.. although I have had no problems when doing so.