You can make it a server control by adding runat="server" and it will be available in your code behind file. OR if you don't prefer this then use Request.Form["Name"] in your code behind file. Here "Name" is the name you are giving to your textbox control.
In your case the name is StartDate
So try to access the value of textbox from the code behind using Request.Form["StartDate"]
Read this article.. https://www.aspsnippets.com/Articles/Get-value-of-HTML-Input-TextBox-in-ASPNet-code-behind-using-C-and-VBNet.aspx