rebellion's answer above won't actually work, because to CSS, 'background-position' is actually shorthand for 'background-position-x' and 'background-position-y' so the correct version of his code would be:
$(document).ready(function(){
$('#submenu li').hover(function(){
$('#carousel').css('background-position-x', newValueX);
$('#carousel').css('background-position-y', newValue);
}, function(){
$('#carousel').css('background-position-x', oldValueX);
$('#carousel').css('background-position-y', oldValueY);
});
});
It took about 4 hours of banging my head against it to come to that aggravating realization.