Could be anything! Wrong CSS path, code error, you name it. We wouldn't be able to help unless you give us a link to your site so we can check it.

Also, http://css-tricks.com/how-to-ask-a-good-question-in-the-forums/

The CSS styles for <HEADER> (as they are written in style.css) are definitely applied, this is what I see:

header {
display: block;
border: solid thin blue;
background-image: url(images/header.jpg);
height: 206px;
background-repeat: no-repeat;
width: 900px;
background-position: top center;
}

However the styles you described for #nav-menu and #nav are not, because you did not give any element the id "nav-menu" or "nav". Perhaps you meant nav instead of #nav?

Stylesheet is linked though: http://homerunlogo.com/test/wp-content/themes/CustomAaron/style.css does not lead to an error page.

On the other hand

<link rel="stylesheet" type="text/css" href="data:text/css,">

is not linked in the head