Seems straightforward in the AirPort software, there is a dropdown for "Extend" and then login and password for the existing WiFi network, but still errors out at the last moment when doing the setup.
How old is router? I ask because until about 3 years ago did mass routers started accepting jumbo Fames (1500MB bits in frame) to make up an IP! That means if your router is more than 3 years or older it probably won't do jumbo frames!