I have a "problem" with my internet connection. Someone help me please?

[Philidor]

It's not really much of a problem, but it's really annoying.

I share the internet connection with my dad's computer using an Nway Switch, so the type of connection my computer uses to connect to the internet is a Local Area Network. However, the computer randomly tries to connect by an internet connection. I choose cancel and can continue browsing websites, showing that it is not necessary. The thing is that it stops all loads until I hit cancel. It's becoming really annoying.

I think this happened because we thought we would need an internet connection (not LAN) in order to be able to connect to the internet. Know what I mean? How do I get rid of that connection?