Well, I still can't get it to connect to my main wifi network (router), but I have managed to get it to connect to the other wireless network (Time Capsule).
No idea why 2 out of 3 AEs will connect to the main wireless network, but this one won't. All the settings are the same in Airport utility 6, and they are all running the latest firmware.
To get it to (sort of) work, I held the reset button down as I switched on the power, and kept the button pressed until the light went off.
I connected wirelessly to the AE's own Airport ID from my iMac, and set up the name and password, also the wireless settings. Airport Utility said "update failed", as it wouldn't connect to the wireless network.
I then connected using ethernet, and changed the wireless settings so that it connected to the Time Capsule.