My three year old Airport Extreme Base Station stopped working last week. It was dead with no blinking lights. My first impulse was to tear it open and see if there was a loose power connector, but after getting the bottom off, I saw difficulty in disassembling it further. Luckily, it occurred to me to attach my multi-meter to the station's power supply, and eureka, no voltage. The external power supply had failed not the hub itself.
Looking around the web, it seems most places are out of of stock for the AirPort Extreme Base Station Power Adapter (Part number M9479LL). Perhaps many are failing right now. But the Apple online store has it in stock, so I ordered one for $20 and problem solved.