I have been able to connect to Xbox Live for the past month and a half without any problem... Now it wont connect, but it says that it has internet access. All of our computers and our Wii gaming system is connected to the internet, so, do I need to buy a new xbox 360, or is there something I can do to regain access to xbox live?

I have trouble connecting from time to time, and when I do, I restore the network configuration to the factory settings. To do this, go to My Xbox -> Network Settings -> Wired/Wireless Network (whichever you are using) -> Configure Network. Go to the Additional Settings tab, and then down to Restore to Factory Defaults. Click "Yes, restore to factory defaults." Note that it won't touch any of your game data, only the network settings, so the warning it gives is nothing to be concerned about. This may or may not work for you, but it's definitely worth a shot. If all else fails, just call Xbox (1-800-4-MY-XBOX [US]) and they should be able to sort you out.
Hope this helps!