Having a similar problem with a MacBook Pro and a Time Capsule(which is an Airport Extreme with an NAS hard drive in it):
My Setup:
Cable >>> Cable Modem >>> Time Capsule >>> Wireless and Wired Client Machines
Before I setup my new Time Capsule, my MBP was not able to connect to the previous router using Ethernet. I thought maybe my Ethernet port had fried, but it turned out that the DHCP settings on the MBP got messed up be because I had used a Verizon wireless broadband card and its Location settings under Network Preferences, were overriding the 'Automatic' settings. Once I put the Location back to Automatic, it seemed my Ethernet was working again.
I installed Time Capsule, which was amazingly able to connect to the Internet through the cable provider without using PPPoE, which I did not know it could do. My MBP was assigned an IP address of 10.0.1.2 via Ethernet, and Airport client automatically turned off. Great!
Then I tried to do a backup with Time Capsule. This part proved to be a nightmare, and I still haven't been able to complete a first backup of my machine.
Time Capsule (as a Network Access Storage device, NOT as Airport router) would dismount midway through backup - gone! - and it's because my Ethernet IP address settings suddenly switched to 'self-assigned' IP address, and with Airport turned off, unable to connect to my LAN (10.0.1.x range).
I tried Manually assigning a 10.0.1.5 address to my Ethernet settings, but it won't connect.
I rebooted the machine a few times, messed with the DHCP settings for both the Time Capsule and the MBP, and I was even able to get Ethernet working temporarily, but within an hour, BOOM, Ethernet back to 'self-assigned' IP address, and I'm only able to connect to the Internet via WiFi, because using Airport as my Network client, I am assigned a proper LAN IP address of 10.0.1.2.
So, now I'm backing up my MBP for the first time to Time Capsule and it has taken ALMOST 24 HOURS ALREADY!!!
NOTE TO APPLE: MAYBE YOU SHOULD ALLOW THE TIME CAPSULE TO CONNECT TO THE COMPUTER VIA USB OR FIREWIRE FOR FIRST BACKUP!!! This is ridiculous for how much I paid for the Time Capsule.
So, is the problem with Time Capsule/Airport base station technology, or is it with OS X and the client computer??? Considering I was having this kind of problem using a Linksys router, well before I installed Time Capsule, makes me think it is the latter.
In fact, I have a printer and a WinXP machine on the same LAN, and they have no problem receiving proper IP addresses from the Time Capsule. It is only the MBP and only the Ethernet connection. Connecting to the Internet via WiFi is great at the airport, but it is woefully inadequate when you have to upload and download files constantly for a living. Slllllooooowwwww.
Folks, if you are having trouble with self-assigned IP addresses, try some of these possible solutions:
http://discussions.apple.com/thread.jspa?threadID=1417058&tstart=0
I consider this a serious bug that Apple needs to address. Why doesn't DHCP work right in OSX?