Let's go back to the start and explain some basics here.
In order to connect to the Internet, one would need an Internet Service Provider (ISP, for short). An ISP can be many things - a Cable connection, DSL from the phone company, a cellular-based wireless connection from a mobile broadband provider, etc.
In your case, it sounds like you have DSL. DSL runs through the phone lines and typically a computer would connect to it with a network cable. In some cases, the DSL provider will give you a combination modem and wireless router. This will enable you to connect to the DSL modem through a wireless 802.11-based connection. My guess is that this is how your Dell notebook connects.
In your case, I believe you'll just need to see how your Dell laptop is connected to the Internet.
You can not just buy a laptop, open it up and expect a spontaneous Internet connection.