Verstraeten, you don't say which type of internet connection you have, so this is difficult to answer.
Check your Startup Folder (Start Button > Programs > Startup) and check that there is no link there to your connection.
The most likely reason why your PC is trying to connect is that an application launches on Startup which is trying to use the internet. You could experiment and remove links from your Startup folder. You could also check for Viruses and Spyware as these could be causing this.
If none of the above works, you could look at the System Configuration Utility (Windows XP). Run this by pressing Start > Run and typing "MS Config"
Russell Hinch, March 2004