Make an asp .net web app offline

You can do that on global.asax as:

protected void Application_BeginRequest(Object sender, EventArgs e)
{
   if(DateTime.UtcNow > cTheTimeLimitDate)
   {
        HttpContext.Current.Response.TrySkipIisCustomErrors = true;
        HttpContext.Current.Response.Write("...message to show...");
        HttpContext.Current.Response.StatusCode = 403;
        HttpContext.Current.Response.End();
        return ;    
   }    
}

this is safer than place it on web.config, but nothing is safe enough. Its even better there to redirect them to a page, or not show them a message, or what ever you think.

For make redirect to a page you also need to check if the call if for a page, and the code will be as:

protected void Application_BeginRequest(Object sender, EventArgs e)
{
   string cTheFile = HttpContext.Current.Request.Path;
   string sExtentionOfThisFile = System.IO.Path.GetExtension(cTheFile);
   if (sExtentionOfThisFile.Equals(".aspx", StringComparison.InvariantCultureIgnoreCase))
   {
     // and here is the time limit.
     if(DateTime.UtcNow > cTheTimeLimitDate)
     {
        // make here the redirect
        HttpContext.Current.Response.End();
        return ;    
    }    
  }
}

To makes it even harder, you can make a custom BasePage that all page come from it (and not from System.Web.UI.Page) and you place there the limit on the render of the page - or show a message on top of every page render, that the time is ends.

public abstract class BasePage : System.Web.UI.Page
{
    protected override void Render(System.Web.UI.HtmlTextWriter writer)        
    {
        if(DateTime.UtcNow > cTheTimeLimitDate)
        {
            System.IO.StringWriter stringWriter = new System.IO.StringWriter();

            HtmlTextWriter htmlWriter = new HtmlTextWriter(stringWriter);

            // render page inside the buffer
            base.Render(htmlWriter);

            string html = stringWriter.ToString();

            writer.Write("<h1>This evaluation is expired</h1><br><br>" + html);         
        }
        else
        {
            base.Render(writer);
        }
    }
}