Airport Extreme Flashing Amber - but internet connection is OK

I have the current generation of Airport Extreme, which has been working just fine, until tonight. It started flashing amber. My internet connection is OK, and in fact my desktop is connected to the internet thru the Airport Extreme via ethernet cable, so that pathway works (which rules out faulty cable between Airport and modem). But the amber light keeps flashing, and none of my devices that connect via WiFi can connect to the internet (to be clear, they can see my base station, but they cannot connect to the internet. The only device that can connect is my desktop, which again is connected to the base station via ethernet cable). I've done multiple power-cycles, and a hard re-set of the base station, same result. In Airport Utility, the error is "Your Apple Wi-Fi base station does not have a valid IP address", but assuming that this is the correct error (which I am doubting, since I am connected to the internet), there is no way for me to address it.

I have two Airport Express's on this network - needless to say, they are also showing up as problems in Airport Utility since their base station is amber.

BTW - I am running OSX 10.6.8 - OK, I'm a dinosaur. But just in case that was the problem, I tried to address this with the current Airport Utility from my iOS 7 iPad, but still no luck.

Any advice?