Starting with the basics (assuming Windows 95 through XP, IE, 5.5 or 6), for unwanted dialup connectoids: (these procedures may not do it for your specific symptoms, but start with them anyway.)
From IE menu line: Tools>Internet Options>Connections.
1. Ensure there is a dot beside "Never Dial a Connection". 2. In "Dialup and VPN Settings" window, are there connectoids listed there that you don't use? Delete them. Make sure that the correct Earthlink connectoid is set as the default. The connectoid that is always popping up, and doesn't work properly anyway, may have incorrect proxy settings listed. Call Earthlink tech support if you're not sure of what you're seeing. (If you have a high-speed connection, you don't need any dialup connection here, since the highspeed is a network interface and doesn't use the Dialup Networking at all. ) 3. Still in Internet Options, go to the General tab, click on Delete Files> check Delete All Offline Content>OK, when that's done click Delete Cookies, then OK.
Another frequent culprit is Outlook Express. Tools>Accounts>Properties>Connections>ensure NO checkmark on "Always connect to this account using" line, if a dialup connection is selected and that box is checked OE will try to make a dialup connection even if you are already online with highspeed.