Replace your css code as mentioned below:
.breadcrumbs > li{
display:inline-block;
vertical-align: middle;
}
.breadcrumbs > li:first-child a{
background: transparent url("../images/home_image2.png") 0 0 no-repeat;
width: 16px;
height: 13px;
display: inline-block;
}
It should solve your issue. Also it will help your home icon to behave appropriately as a link for user, putting here inside 'a' tag instead 'li' tag.
---Update--- Forgot to mention, change the height / width value to your icon image, the css have the ones which I had of my icon.