See this sample page.
The icon I want to be using is this:

The icon, as shown on the page, looks like this:

How can I make DatePicker use my original icon without modifications?
See this sample page.
The icon I want to be using is this:

The icon, as shown on the page, looks like this:

How can I make DatePicker use my original icon without modifications?
You need to set the buttonImageOnly property to true, like this:
$('#datepicker').datepicker({
showOn: 'button',
buttonImageOnly: true,
buttonImage: 'http://dl.dropbox.com/u/464119/kuzando/datepicker/calendar.png'
});
buttonImageOnly: Set to true to place an image after the field to use as the trigger without it appearing on a button.