I have a broadband connection which is connected to one computer. From that computer I would like to share my internet connection with the other computer which is in LAN.

It will be easiest if you hook up the modem directly into the router and then connect the router to the computers. This way, you are not having to share a connection through a computer, which then has to be powered on to get online.

Firat you need to but a router. You plug the madem to the LAT port and the other computer to the remaining ports on the router

If you really want to share the network connection through a single computer then you should utilize the network address translation (NAT Routing) feature of Windows. If you have a desktop, install a second network adapter and hook that directly into a router. The IP address of that adapter should be configured as the gateway for the other systems sharing the connection.

I am sure there is a way to do it, but i would strongly recommend to get a router. You can get them really cheap and they're the easiest thing to install. All you have to do is plug in the DSL modem to the router via ethernet cable, and then plug in the computers to the open ports on the router, and that way you'll be online on either machine without the need of both machines being on.