You could read the Request.QueryString["s"] parameter, even when it is a post, the SearchBoxEx adds it.
Edit
Based on the comments and new info, are you using 'pure' javascript? This would be a jquery example:
<a href="#" onclick="newSearchResultsPageWithScope(); return false">Search</a>
WARNING: You should change the site masterpage INSIDE your site with SharePoint designer, not the one in the C:\Program Files\etc... folder. You could also navigate to the
http://yourportal/_catalogs/masterpage
library and download a copy of the default.master to change it then upload it back to the library, do all this carefully, you can break your sharepoint very easily.
Insert above the </HEAD> tag in your masterpage:
<script type="text/javascript" src="http://jqueryjs.googlecode.com/files/jquery-1.3.2.min.js"></script>
<script type="text/javascript">
function newSearchResultsPageWithScope()
{
var scope = $(".ms-sbscopes select").val();
location.href = "/CustomResultsPage.aspx?s=" + scope;
}
</script>
The jquery portion is pretty straightforward, it gets the <td> with the class="ms-sbscopes", and the <select> element under it, then it sets the 'scope' variable to the selected value of the scopes dropdown.
Also, customizing the masterpage in a sharepoint site is fine, do not worry with that.