O.K. I think I've got it. At least for Windows ME.
Close all windows except the minimized one.
Right-click on an empty portion of the task bar.
Select "tile windows horizontally".
If the window is not maximized, maximize it.
Hold down Shift and close it.
That should do it.
Also do this.
Right click on the IE icon on the taskbar.
Select Properties.
Where it says Run, be sure Maximized is selected.
DonM