I run three airport units in my house and while updating two airport express units to the new firmware 7.6.3 one of the units shut down and now won't start back up. I've tried the obvious things like plugging-unplugging then hitting the re-set but no luck.
There are three Airport resets, soft, hard and factory default. It would probably be beneficial if you tried each one in sequence. Actually, you could jump to the factory default reset if you don't mind reconfiguring from scratch.