You're in IE7, are you sure you're not just opening another tab in the same window? Tabbed browsing is a new feature--turned on by default--in IE7.
To open a new window, Ctrl + N or File->New->Window usually does the trick nicely. You could also try the IE icon again on the Desktop/Quicklaunch bar. To force a web link to open in a new window, rather than a tab or the same window, right click and select "Open in New Window".
If your using a special internet key on your keyboard, I've noticed that it behaves oddly on mine. If I don't have IE open, it will open an instance, but if I have one up, it will send me to my home page. Oddly enough, if I minimize all actives IE sessions, it will open a new one. :?
Hope that helps.