Sometime ago, I also encountered the problem where the Dial-Up Internet dialogue box kept popping up, while I was surfing or doing my work. This annoying popup problem doesn't seem to go away.
Why Connect Broadband Connection keeps popping up?
As for me, it was because the other day, I accidentally unable my Broadband connection. Then I went to Network Internet access and I tried to connect it via Broadband connection.
How to stop "Connection Broadband Connection message from popping up
1. First go to Start.
2. Click Control Panel.
3. Next click Network and Internet.
4. Now click Internet Options.
5. A menu box called "Internet properties" will pop up.
6. Select on "Connections" tab" on the top.
7. Now you should see the option: "Dial whenever a network connection is not present" is checked. In other words, you see the small circle in font of the sentence is with a blue dot.
8. What you do is click on the first option: "Never dial a connection".
9. Finally click "Apply" and then click "OK".
That should stop get the Connect Broadband Connection box from popping up again.