First test if your Internet connection is down or if it just Internet Explorer that can find a website.
Go to DOS If windows XP/vista under the start/windows logo bottom left click than and within the search (Vista)/run(XP) box type CMD and hit enter on your keyboard.
You will get a black window box to show up type ping www.yahoo.com do you get something that looks like this?
Reply from 209.###.###.### bytes =32 time=
4 times?
if yes then you have internet if NO then you need to stop here and call your Internet Server Provider to assist you with getting your HighSpeed Modem back online.
IF YES.
Then Open IE
Click the Tools Menu item and select Internet Options
Select the COnnections tab
Remove all Dial-up Connections that you seel listed
Then select Never dial a connection
after that select LAN settings
Remove all check boxes and select OK
Click Apply and OK once more. Close and Re-Open IE
Let us know if this doesn't work.