wrote:

my shortcut to

"c:\program files\internet explorer\iexplore.exe" www.ancestry.com

will not work (fails to connect).

"Fails to connect" means what? That IE doesn't load? That you see an
error message of "program not found"? That IE load and issues an error
message? What?

That command works on every computer I use at home and work. The format
is "path\iexplore.exe url".

What I showed uses the default path for IE on Windows XP. I don't know
where iexplore.exe is located on your host. You will need to specify
whatever path of where is iexplore.exe on your host.

and my shortcut to

http:\www.ancestry.com

Which means you are using whatever is configured as the default web
browser and which may not be IE.

connects, but acts the same way - ie minimized window, and maximizing
it is not remembered.

You first need to be sure you can run iexplore.exe from wherever it is
located on your host. Only you know what security software you might've
installed or what tweaks you applied that might affect registry entries
for loading IE from the registry entries. Load IE from the command line
and see what happens from there.

Have you tried loading IE in its no add-ons mode?
Have you tried rebooting into Windows' safe mode (with networking)?