Rumen,

 Thank you for your reply.  You proposed an alternate and perhaps more direct solution for my need.  So this is almost the answer that I am looking for.  But I also asked how to perform a client-side action:  "So can anyone show me how in a client-side script to respond to a row change in a webgrid, and then update a control (the hidden textbox) from a column in the newly active row." 

Your solution looks as if it will solve the scenario I described, but am also looking for how to implement a clientside script on rowchange to read a cell value in the active row and update a second control with that value.  Any thoughts?

This is an interesting case - I took the time to recreate it locally and had some good progress with it. The idea is to handle the OnClick event of the grid - it fires when end-users click on the grid row/cell/column. Then, in the postback  event handler you can bind your second grid based on the row clicked in the first one. The second grid can be placed inside an UpdatePanel or WARP with Triggers set to the fist grid - this will make sure the partial update take care only of Grid #2.

 Here is my code:

 
   <igtbl:UltraWebGrid ID="UltraWebGrid1" runat="server" Height="200px"
        Width="325px" onclick="UltraWebGrid1_Click">
    </igtbl:UltraWebGrid>
   
    <br />
   
    <asp:UpdatePanel runat="server" ID="UpdatePanel1">
        <ContentTemplate>
             <igtbl:UltraWebGrid runat="server" ID="UltraWebGrid2" Visible="false">       
            </igtbl:UltraWebGrid>       
        </ContentTemplate>
        <Triggers>
            <asp:AsyncPostBackTrigger ControlID="UltraWebGrid1" EventName="Click" />
        </Triggers>
    </asp:UpdatePanel> 

    protected void Page_Load(object sender, EventArgs e)
    {
        DataTable dataTable = new DataTable();

        dataTable.Columns.Add("ID");
        dataTable.Columns.Add("Decimal");

        dataTable.Rows.Add(new object[ { 1, 1.44 });
        dataTable.Rows.Add(new object[ { 1, 1.47 });
        dataTable.Rows.Add(new object[ { 1, 1.48 });

        UltraWebGrid1.DataSource = dataTable;
        UltraWebGrid1.DataBind();

        //ultraChart.Page.Form.Controls.Add(ultraChart); 
    }




    protected void UltraWebGrid1_Click(object sender, ClickEventArgs e)
    {
        if (e.Cell != null)
        {
            int rowIndex = e.Cell.Row.BandIndex;

            UltraWebGrid2.Visible = true;

            DataTable dataTable = new DataTable();

            dataTable.Columns.Add("ID");
            dataTable.Columns.Add("Decimal");

            dataTable.Rows.Add(new object[ { 1, rowIndex });
            dataTable.Rows.Add(new object[ { 1, rowIndex });
            dataTable.Rows.Add(new object[ { 1, rowIndex });

            UltraWebGrid2.DataSource = dataTable;
            UltraWebGrid2.DataBind();

        }
    }

Hope this helps.