This feature is actually built-in to the core, granted you need to toggle some of the default settings on the breadcrumbs control. It's alot easier than the core modification I was just writting as a sample.

Anyways, you'll want to modify your active skin, and add something like this into the file...

<script runat="server" language="VB">
    Private Sub skinpageload(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
        If DotNetNuke.Common.GetPortalSettings.ActiveTab.TabID = DotNetNuke.Common.GetPortalSettings.HomeTabId Then
            dnnBREADCRUMB.RootLevel = "0"
        Else
            dnnBREADCRUMB.RootLevel = "-1"
        End If
    End Sub
</script>

The text "Root" will be used by default from the Localization file, you can override this setting to change the name of the home page through the Host > Languages module.

It's hidden deep, took me a second to find the exact path... 

Host > Languages > Edit Default Language > Edit Language Files > Local Resources > admin > Skins > App_LocalResources > BreadCrumb.ascx

After all those clicks, Root.Text is the only item in the file