L ho provato in locale e funziona.
Ho modificato con questo
xmlhttpRequestFunc.setRequestHeader("Content-type","application/x-www-form-urlencoded");
perche' mancava Content-type
e lo status a 200 con if(xmlhttpRequestFunc.status == 200){....
Così com'e' scritto, response.php deve stare allo stesso livello del file che lo utilizza oppire dargli il path/url assoluto.

Questo il mio
codice:
<script type="text/javascript">
function getXML_HTTP(){
    var xmlHTTP = null;
    if(window.XMLHttpRequest){
        xmlHTTP = new XMLHttpRequest();
    }else if(window.ActiveXObject){
        xmlHTTP = new ActiveXObject("Microsoft.XMLHTTP");
    }
    return xmlHTTP;
}

function getConnectionResponse(){
    var xmlhttpRequestFunc = getXML_HTTP();
    var pageURL = "response.php";
    var logusername = document.getElementById("logusername").value;
    var logpassword = document.getElementById("logpassword").value;
    var logdata = 'logusername='+logusername+'&logpassword='+logpassword;

    xmlhttpRequestFunc.open("POST", pageURL ,true);
    xmlhttpRequestFunc.setRequestHeader("Content-type","application/x-www-form-urlencoded");
    xmlhttpRequestFunc.send(logdata);
    xmlhttpRequestFunc.onreadystatechange = function(){
     if(xmlhttpRequestFunc.readyState == 4){
         if(xmlhttpRequestFunc.status == 200){
            var htmlElement = document.getElementById("feedback");
            htmlElement.innerHTML = xmlhttpRequestFunc.responseText;
         }
        }
    }
}
</script>

<div id="wrapper">
        <div id="form">
            <form action="response.php" method="post">
            <label>Username</label>
            <input type="text" name="logusername" id="logusername">
            <lable>Password</lable>
            <input type="password" name="logpassword" id="logpassword">
            <input type="submit" name="logsubmit" id="logsubmit" value="LOGIN" onclick="getConnectionResponse();return false;">
            </form>
            <div id="feedback">xxxx</div>
       </div>

       </div>
PHP
codice:
<?php
if(isset($_POST['logusername']) && isset($_POST['logpassword'])){
        $logusername = $_POST['logusername'];
        $logpassword = $_POST['logpassword'];
        if(empty($logusername) || empty($logpassword)){
            echo "enter username and password";
        }else{
            echo "your name is ".$logusername." and your password is ".$logpassword;
        }
    }