cancella l'evento Page_Load e poi:

ASPX
codice:
<form id="form1" runat="server">
    <div>
        <asp:TextBox ID="txt1" runat="server" Style="width: 200px" Height="25px" />
        <asp:Button ID="myButton" OnClick="submit" Text="Submit" runat="server" />
        <asp:Literal ID="lt" runat="server"></asp:Literal>
        <div id="div1" runat="server" style="display:none;">
            Ciao sono il DIV
        </div>
    </div>
</form>

VB
codice:
    
Protected Sub submit(sender As Object, e As System.EventArgs) Handles myButton.Click
        lt.Text = txt1.Text
        div1.Attributes.Add("style", "display:block;")
End Sub