I've repaired lots of Xboxes lately with damaged ethernet. This time of year is bad for the Xbox NIC and they are often damaged by static electricity or power surges.
If you get no green "link" LED on the Xbox NIC and your router, or if your "activity" LED is always on, and you get a "no link" or 0.0.0.0 IP address on your Xbox, then replacing the ethernet PHY will usually fix this issue.
This fix applies for all Xboxes, from 1.0 - 1.6b.
You will need good soldering skills, because if you damage the solder pads for the PHY chip, then is will be very difficult or impossible to repair.Here is the chip you will be removing and replacing with a good one:

Make sure you orient the chip correctly when installing. The small circular dot or indentation in the chip is pin1, and will match up to a silkscreened indentation on the motherboard.
PHOTO.
The procedure for removing and installing the chips is very similar to doing a RAM upgrade. You can check
this thread for links to removal and install videos.
In short, remove the old chip carefully, without damaging the solder pads on the motherboard. Then line up the new chip, solder down one corner pin, then line up and solder down an opposite corner pin. The rest of the pins should line up, and you can solder them down one at a time.
I sell replacement ICS PHY chips (tested and professionally removed with a SMT station, not as shown in the video) for $18 plus shipping. I also offer a full repair service for $40 plus return shipping (covers the ICS chip and port replacement if needed).