I assume you're connecting via ethernet, and that the LAN card is working correctly.
If you go through a Windows powered machine to get to your internet, you'll need to config that machine to allow ICS. (Internet connection sharing). If your computer is connected to a router (not directly to another PC) you'll have to setup your Linux box (the one you metioned) to get it's IP via DNS. (Most routers are setup to use DNS by default, and if you haven't messed with it, you should have this setup as well.)
There is most likely an icon in the config menu for your "Network Settings" or "Lan Settings". Go there and see if you can make the changes (or verify the settings) that I mentioned. If you're connecting through another computer, make sure you have ICS setup.
Best of luck.