Windows Explorer is a file manger and also responsible for showing the desktop, so you can't disable

Windows Explorer is a file manger and also responsible for showing the desktop, so you can't disable or stop that program without serious repercussions.

Or do you mean the Internet Explorer browser (IE)?

If that program isn't running then it shouldn't cause issues.

You can use the MSConfig program or the Autoruns utility to see which software gets started.

http://technet.microsoft.com/en-us/sysinternals/bb963902.aspx