Well my (old) UFO shaped 802.11g Airport Extreme seems to be not working despite the three lights on the front flickering and flashing away.
Despite power cycling the base station, it would not broadcast a wireless signal and even when connected by ethernet it only appeared sometimes in the Airport Utility.
I may do a full reset, but in the meantime I have replaced it with my spare Airport Express which I usually take away with me when staying in hotels or need to use at conferences.