Connected on LAN but keep getting dial-up prompt

I have a dial-up connection in my list of Network Connections. I can't even
remember that last time that I used it, because I'm usually connected via
broadband, either wired (Ethernet) or wireless.

However...

A couple of days ago, I had to create a new dial-up connection for a
different ISP, which I only used for several minutes (and may use again,
occasionally).

But now, even though I'm connected via Ethernet to the Internet, every
couple of minutes I get a prompt to connect to that new dial-up network
connection. My Internet stops working until I press "Close" on the prompt.

I noticed that the new dial-up had registered itself as the Default
Connection. I selected "Cancel as Default Connection", but the prompt still
keeps appearing.

How can I stop the computer from prompting me to dial up even though I'm
already connected via broadband?