A fade will always fade every element under and including the one you selected with jQuery. Unless the div you want to stay visible is directly under the body, this will be tricky. To achieve the effect you desire, you should clone the div you want visible, and absolutely position it in the same location as the original. That also means you'll need to put the main content that is getting hidden inside of a container div, so instead of fading the body, fade the container div, and put the cloned div at the top level directly under the body, after the container.
<body>
<div id="content-to-fade">
...<div id="div-i-want-">...</div>
</div>
<div id="copy-of-div-i-want">...</div>
</body>
so in the example, you would create "copy-of-div-i-want", append to the body and then call fadeTo on "content-to-fade".
This technique is a pretty common way of implementing drag and drop, because the copy can easily and efficiently be absolutely positioned around the screen.