Hi  aspsun11,
To run JavaScript code on browser close follow the below steps.
1. After successfull Login set Session variable to identify the user. In the example i have used IsValidLogin and UserId.
2. Then create a JavaScript function to make AjaxCall to a page on browser close.
3. Then call the JavaScript function and pass the required parameter.
Check this example. Now please take its reference and correct your code.
JavaScript
function AjaxCall(userId) {
    var webUrl = 'Delete_Record.aspx?UserID=' + userId;
    var xmlHttpObject = null;
    try {
        // Firefox, Opera 8.0+, Safari...
        xmlHttpObject = new XMLHttpRequest();
    }
    catch (ex) {
        // Internet Explorer...
        try {
            xmlHttpObject = new ActiveXObject('Msxml2.XMLHTTP');
        }
        catch (ex) {
            xmlHttpObject = new ActiveXObject('Microsoft.XMLHTTP');
        }
    }
    if (xmlHttpObject == null) {
        window.alert('AJAX is not available in this browser');
        return;
    }
    xmlHttpObject.open("GET", webUrl, false);
    xmlHttpObject.send();
}
Login.aspx
<asp:Button Text="Login" runat="server" OnClick="Validate" />
 Login.aspx.cs
protected void Validate(object sender, EventArgs e)
{
    // If Valid Login.
    if (1 == 1)
    {
        Session["IsValidLogin"] = true;
        Session["UserId"] = "12345";
        Response.Redirect("~/Default.aspx");
    }
}
Default.aspx
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title></title>
    <script src="BrowserCloseCall.js" type="text/javascript"></script>
    <script type="text/javascript">
        window.onunload = function () {
            AjaxCall('<%= Session["UserID"] %>');
        }
    </script>
</head>
<body>
    <form id="form1" runat="server">
    <div>
    </div>
    </form>
</body>
</html>
Namespaces
using System.Configuration;
using System.Data;
using System.Data.SqlClient;
Delete_Record.aspx.cs
private void Page_Load(object sender, System.EventArgs e)
{
    // If user logged in.
    if ((bool)Session["IsValidLogin"])
    {
        // If UserId is exists.
        if (!string.IsNullOrEmpty(Request.QueryString["UserID"]))
        {
            string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
            using (SqlConnection con = new SqlConnection(constr))
            {
                using (SqlCommand cmd = new SqlCommand("DELETE FROM Table WHERE UId = @UserId"))
                {
                    cmd.CommandType = CommandType.Text;
                    cmd.Parameters.AddWithValue("@UserId", Request.QueryString["UserID"]);
                    cmd.Connection = con;
                    con.Open();
                    cmd.ExecuteNonQuery();
                    con.Close();
                }
            }
        }
    }
}
After login IsValidLogin and UserId is set and redirect to Default page.
When user close browser AjaxCall is executed inside window.onunload function and Session["UserID"] is passed and Delete_Record page called and record deleted from table.