Do you have a wireless router?

If you do, you have to plug the DSL modem into the router, and then the laptop should get access wirelessly. It wouldn't matter then if the Local Area Connection is unplugged, as you're not using that connection. Don't remove the driver though-- it's not interfering.

Yes. The Local Area Connection will be the Ethernet (wired) network card in the laptop; the wireless connection will be a separate entry in your Network Connections setup.
Is there an entry in your Network Connections for "Wireless Network Connection:? If so, does its status show as "Enabled"?



That's a little unclear; could you please be more specific about what you mean by "unless DSL line is connected" and describe your whole Internet connection wiring configuration in more detail?