Unassigned IP Address

I recently upgraded to a gigabit router, with the intention of having my various computers and backup devices all wired in together and backing up at gigabit speeds. The router (a Billion 7800N) worked great, and the wireless-N speeds are very nice indeed. However, when it came to connecting to my Mac using an Ethernet cable all I got was:

Unassigned IP Address 169.x.x.x

I’d actually experienced this before while staying in a hotel and trying to use their free internet but had assumed it was the hotel’s problem. Not what I wanted to see from a new router.