Assuming that all your dropdwons is in the form named "myform" and form action either empty or defined as your page, try this:
<% Set conn = Server.CreateObject("ADODB.Connection")
conn.connectionstring = "Provider=Microsoft.Jet.OLEDB.4.0;" &_
"Data source = \\ mockcourt.mdb"
Conn.Open
set rs=Server.CreateObject("ADODB.recordset")
dim Scn
Scn=request("ListBox1") & "" ' to make sure that Scn is not null in any case
%>
<select NAME="ListBox1" onChange="clname(this)">
<% Set rs = conn.Execute("SELECT * FROM school")
Do While Not rs.EOF ' define the ListBox OPTIONs
if Scn=rs("schoolKey") then%>
<OPTION VALUE="<%= rs("schoolKey") %>" selected> <%= rs("school") %></option>
<% else %>
<OPTION VALUE="<%= rs("schoolKey") %>"> <%= rs("school") %></option>
<%
end if
rs.MoveNext
Loop %>
</SELECT>
<% set rs=nothing %>
<script type="text/javascript">
function scname(target){
var Scn = target.value
alert("You changed to "+ Scn)
document.forms["myform"].submit();
}
</script>
<SELECT NAME="ListBox2" SIZE=1>
<%
set rs=Server.CreateObject("ADODB.recordset")
Set rs = conn.Execute("SELECT * FROM class WHERE school = '"+Scn+"'")
Do While Not rs.EOF ' define the ListBox OPTIONs
tba=Scn %>
<OPTION VALUE="<%= rs("school") %>,<%= rs("classname") %>"> <%= rs("classname") %></option>
<% rs.MoveNext
Loop %>
</select>
<% set rs=nothing
conn.Close %>
it is considered a good practice to have HTML tags, inputs closed even images. And if you planning to ever work within companies where they have to obey certain standard make it your habit.