Windows will attempt to initiate the default dial-up connection whenever it thinks that it is not connected to the internet, and an internet request is made.
It would seem that the current default dial-up connection is the M-Web connection, so windows keeps trying to start that one.
Change the default dial-up connection to the new one, or remove the MWeb ones' "Default" setting.
In addition, there is a setting in Internet Explorer where you can force it to initiate a dial-up connection before it will begin browsing, you may want to check there for that setting and disable it or choose the new connection.
I know how to do this in WinXP Pro, let me know if that's the operating system you're using.