We have two iMacs in the study. Also an Airport Extreme wireless router. The new iMac sees the router, delivers the internet, no problem. The old iMac can't see the wireless network. I've checked the seating of the airport card and antenna. All seems fine. The Mac says that Airport is working, but isn't connected to a wireless network. Trying to connect to the wireless network (with its regular password) fails.
OK, here's the freaky bit. If I use the Airport Setup Utility, the old iMac instantly spots the Airport Extreme, gives it its correct name, can interact with it and reboot it etc.
I have tried things like turning airport off and on, rebooting, and so on, and have checked all settings. Plugging in an ethernet cable gives Internet; it also gives a tripwire across the study floor.