Does the laptop show that the network cable is connected and you just can't get to the Internet, or does it not even show that the cable is connected.  You may need to power off and then power on your modem as sometimes they don't release the IP address that was given to whatever was previously connected to it.

The laptop is not detecting the LAN connection at all. I tried switching of the modem and restarting the lappy, though the LAN was detected in the modem while booting, it subsequently became inactive. When i try connecting the cable to other lappy, the light in the modem for LAN detection glows. Can you help me in sorting this.

I almost sounds like the LAN adapter is disabled in Windows.  Since it's showing a link during the boot process I would guestimate that the adapter is good, but since it goes away when Windows loads, it sounds like it's disabled.  I would say try going into the Network and Sharing Center, click the link on the left for "Change adapter settings" and see if your LAN adapter is listed there.  If so, try right-clicking on it and see if there's an "Enable" option listed.  If so, click it and you should be good.