Probably easy question about a connection.

Hey there guys, I got a bit of a silly question perhaps.

Whenever I restart my router it starts up fine and connects to the internet showing the adsl light and both my computers connect to the router and network between two computers works too.

When I want to connect to the internet with a pc I click the "connect to internet" link so the "online" light on my router starts lighting up. We only have to do this when restarting router so I guess thats normal.

Question:
Why does only my second computer have this connect to internet link at the network connections tab? Whenever I restart my router or if it crashes I have to turn on my second computer to connect to the internet, after that I can turn my second computer off.

Any way to get that connect to the internet button on my first computer as well?