We\'ve tested the Jquery UI (jquery-ui-1.8.10.custom.min.js) Autocomplete function in a simple HTML page which worked.
We then copy the same code into an Asp.net User C
Maybe try using the jQuery.noConflict() method for a test. It basically just makes you use a different alias for jQuery. This worked for me in SF4.3.
var j = jQuery.noConflict();
// Do something with jQuery
j("div p").hide();
// Do something with another library's $()
$("content").style.display = 'none';