Intel Mac :: Why Does It Report A Duplicate IP Address

A few days ago, my wife told me that she was having some serious performance problems on her iMac, and showed me.  While she was doing this, a window popped up announcing that there was a duplicate IP address for the 192.168.1.20 that we'd set her iMac to.  I did a bit of digging, checking all our machines for that address, and trying to contact it to see if it would identify itself.  Everything failed.  None of our machines (that we know of) is using 192.168.1.20, and attempts to contact it via tools like ping, telnet, ssh, and various brousers all report "not responding". 

I changed her address to 192.168.1.21, and the problem went away.  But I'm still worried about the claim that 192.168.1.20 is in use.  This seems to say that there's an unknown machines using it in our house.   

So is there some way that her iMac or either of our Macbooks (or here iPad) can identify it, or at least contact it and give us some clues about what sort of beastie it might be? 

We also have some linux systems, a Windows box, and a couple of smartphones with wifi, and tests from them have also failed, so I'll probably be asking on their lists, too. 

My first suspect was the airport, but I verified that its DHCP server is giving out addresses in the .101 to .199 range that I set it to.  Its config stuff doesn't show the .20 address anywhere that I can find. 

(I did try setting one of the linux systems to use 192.168.1.20, and it didn't report any address conflicts.  I don't know what this tells me.  So I set it back to its original 192.168.1.42 address.  ;-)