it looks like you have the background image applied to the anchor tag:
#links li a {
background-image: url("../images/link_background.png");
background-repeat: no-repeat;
display: block;
padding-left: 36px;
padding-top: 5px;
text-decoration: none;
vertical-align: bottom;
}
the background image for the bullets should be applied to the LI tag instead:
#links li {
background-image: url("../images/link_background.png");
background-repeat: no-repeat;
}