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If you are having issues with connecting your 360 to X-Box live then you would want to try and make sure you have a good Ethernet cable connected to your 360. If you have a modem and it is not connecting you to live. Try unplugging the modem then replugging it. This will reset the IP configuration of your modem to you 360. If you have a Router/Modem, or a Router & Modem, disregard this step.
Also you want to make sure that you have an Internet service provider(ISP). If you don't then you can't connect. If you have a wireless connection for your 360 then I would suggest to call your ISP to make sure you got your wireless router configured properly. Then if it is, I would call 1-800-4MY-Xbox (now this should be last resort as they are slacking in customer service) They will walk you through some basic steps to making sure you are setup properly.
If you are still having issues with Direct Ethernet connection, I would suggest testing your cable on the computer and unplug your modem or router and replug it. If after a few minutes your computer is not connected to the Internet then it is your Ethernet cable. You need a new one. If none of this works. I will try to think of other suggestions for ya.