I have installed Ubuntu on my system, which has two LAN card. One of the LAN card is not working. But the other do work. I have tried configuring the internet connection but failed.
From your comment, I assume, you want to setup a PPPoE connection. This is a method used by some broadband modems to connect a single computer to the internet. You have already connected modem and computer via ethernet and the method works on Windows. You want to know how to do the same with Ubuntu. The fact the you have two network cards could make it harder to get the configuration right? Did I get this?
On modern versions of Ubuntu all network connections are handles by the network-manager. You can access the network manager via its icon (two computers) in the status bar. You can right-click the icon and select "edit connections ..." or similar. This opens a dialog box. The last tab in this dialog reads "DSL" or "Broadband" or similar. Here, click the "Add + " button and enter username + password for your broadband connection.
This is the standard method that you should try first. At the moment, I do not know, how Ubuntu decides which network interface to use. Possible, it will scan all of them for a PPPoE modem.