For starters you should be registering your javascript via the Page's properties in your code behind, rather than adding <script> tags to your markup. That way the file is only included once, even if there are multiple instances of the web part on
a page:
[Code behind]
this.Page.ClientScript.RegisterClientScriptInclude(this.GetType(), "DatePicker", "/_layouts/ChildRecord/date_picker.js");
Secondly, you can't use qualifiers like 'this.txtBirthDate' directly in your markup and expect JavaScript to understand it - the JS will run client side, and the C# will run server side. The ID property of your TextBox is a server side property - if you
want to get the ID that is rendered in the textbox's <input> tag you need to access the ClientId property. Start by adding the hyperlink in your markup:
[ASPX markup]
<asp:HyperLink ID="showCalendarLink" runat="server" Text="Show calendar" />
Then in your code behind set the hyperlink's NavigateUrl property:
[Code behind]
showCalendarLink.NavigateUrl = String.Format("javascript:show_calendar('{0}')", txtBirthDate.ClientID);
In your rendered markup the link href will appear like this href="javascript:show_calendar('ctl00_PlaceHolderMain_txtBirthDate')", so in your JS function you'll have something like this:
function show_calendar(textBoxId) {
var textBox = document.getElementById(textBoxId);
var textBoxValue = textBox.value;
alert(textBoxValue);
}
If this doesn't work then there's a typo somewhere! Hope this helps...
Sam
