I've had this problem for some time but can't resolve it.
Every time I boot up, Windows Explorer also starts up. I've
gotten to the point where I make the window small when I
shut down so it won't open very large when I reboot.
Doesn't matter if I close the window before I shut down;
the Explorer window opens again.

Anyone have any ideas on how to fix this?

You need to take windows explorer out of your startup
folder. I'm not sure exactly where these items are
located except for on the start/programs/startup menu. If
its in there remove it but I know there is another
location for startup items. Maybe this will help