I think the issue was caused by the order in which scripts were being executed on the page. The datepicker needs the JQuery script to be literally the last thing loaded on the page.
And if you have other references to JQuery they need to go ahead of the web assist one.
My test to see if this is the problem is I create a test page right beside the actual form page and input JUST the form on the page. If the date picker does not work on the test page, then we have another problem, but if it works on the blank test page. Then it is probably a script ordering issue.
Give it a try and see if that helps.