Plug by ethernet into a single computer. No other network connections on either computer or AE.
Do a full factory reset.. ie power off.. hold in reset and power on without releasing reset until the LED flashes rapidly.
Don't forget the IPv6 has to be turned on to local link.
And you need Lion or Mountain Lion with latest airport utility.
Thanks for the response. I had done this (by coincidence), but not sure about the IPv6 issue, though. I am using Mtn Lion, so that is not an issue.
As I was messing between plugging ethernet directly into my computer and trying to get my old router re set-up, I noted that the old router did not get recognized by the Airport Utility until I turned WiFi back on (I turned it off when I plugged ethernet directly into the computer). Althought AU recognized my old router, it still did not see the new router (still slow blinking amber light).
Then I noticed in the Airport icon in the toolbar that the new router was showing up there (under Join Other Network or Create Other Network). Once I selected it there, then it showed up in AU. Not sure why it worked this way. I have had 2 prior Airport Extreme Routers (and 2-3 Airport Express) and they all get picked up in AU when originally plugged in.
Anyway, it seems to be working fine now.
Thanks once again for your input.