Solution 1.
Start IE, right click any URL and select "Open in a New Window".
Go back to the first IE window you opened and close it.
Return to the second window and manually drag it to fill the screen. DO NOT USE THE MAXIMISE BUTTON.
Close this second window using the close box.
All IE windows should now open maximized.
Solution 2.
Go to the South Bay Software website and download the TOTALLY FREE AutoSizer 1.71:
Automatically Resize Your Programs - AutoSizer
Quote: "AutoSizer automatically resizes programs for you, keeping them at a specific size or keeping them maximized. One popular use is to keep Internet Explorer maximized when you go on the web."