Here's an example that shows how to add the button using the approach Rene suggested. Note that I specify the url to the image that will be used for the home icon via a css class.
<!DOCTYPE html>
<html>
<head>
<title>Create a Map</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=7, IE=9, IE=10">
<link rel="stylesheet" href="http://serverapi.arcgisonline.com/jsapi/arcgis/3.4/js/dojo/dijit/themes/claro/claro.css">
<link rel="stylesheet" href="http://serverapi.arcgisonline.com/jsapi/arcgis/3.4/js/esri/css/esri.css">
<style>
html, body, #mapDiv {
padding: 0;
margin: 0;
height: 100%;
}
.esriSimpleSliderHomeButton{
border-bottom: 2px solid #666666;
background-image: url(../../forum/images/home.png);
background-repeat:no-repeat;
background-position:center;
}
</style>
<script src="http://serverapi.arcgisonline.com/jsapi/arcgis/3.4/"></script>
<script>
dojo.require("esri.map");
var initExtent;
function init(){
var map = new esri.Map("mapDiv", {
center: [-56.049, 38.485],
zoom: 3,
basemap: "streets"
});
//when the map's loaded add the new button to the slider.
dojo.connect(map,"onLoad",function(){
var initExtent = map.extent;
dojo.create("div",{
className: "esriSimpleSliderHomeButton",
onclick: function(){
map.setExtent(initExtent);
}
},dojo.query(".esriSimpleSliderIncrementButton")[0], "after");
});
}
dojo.ready(init);
</script>
</head>
<body class="claro">
<div id="mapDiv"></div>
</body>
</html>
