Number 1 - If your ethernet cord is going from a modem straight to your 360, then get your modem replaced by your ISP.
This will probobly be free, but if your charged, it will be a small fee.
Number 2 - If you have it going to a routerfrom a modem, then go to your 360 main screen, scroll to the far right 'System' blade, select the 4th choice 'Network Settings', and test your Xbox LIVE Connection. It will ask you to sign out. Select yes.
Results should come up (for wired router)
Network Adapter - Wired
Wireless Network - (Left Blank)
IP Address - Confirmed
DNS - Confirmed
MTU - Confirmed
ICMP - Confirmed
XBOX LIVE - Confirmed
NAT - (either moderate, opened, or strict)
If all those are the same, the problem has nothing to do with the xbox itself and you need a new router, or modem.
If results come out to be
''Network Adapter - Disconnected''
After test is run (and your 360 is connected properly to your router AND modem then you have a hardware problem. Whether the problem is in the 360 or the router/modem is easy to test.
Connect the modem directly to the 360 via ethernet. If this fixes the problem, the router is fail.
If you can get on the internet wirelessly and grounded on a computer, the 360 is busted.
Sorry it took me so long to explain that, but i hope it helps you.
Best of luck