You might try something like this which will set the header background image on all pages and then the more specific rule starting with ".home" updates the header background image on the home page to use just the logo:
#header {
background: url('http://uofweb.files.wordpress.com/2012/11/cropped-universal_or_horiz_k2.jpg?w=720') 0 50px no-repeat;
}
.home #header {
background: url('http://uofweb.files.wordpress.com/2012/11/uof-logo.jpg?w=80') 0 50px no-repeat;
}
Then you can remove the custom header image from your Appearance → Header page separately. If you delete it there, note that you can add a header image back again any time as long as you have a copy of the image so you can re-upload it.