Submit a form in modal box - AJAX

Hello all, I am having trouble submitting a form that is displayed on a DIV that acts like a modal box.

Every time I hit submit, it reloads the page and closes the DIV.

However, if I put a Javascript event-handler, onsubmit="return false" that stops the page from reloading, but I am unable to validate on the server side.

Here is my code and let me know what you guys think....

<div id="modal_window">
    <form name="reg_form" onsubmit="return false" >
    	<fieldset>
        	<legend>REGISTER</legend>
        	<ol>
            	<li>
                	<label>USER NAME:</label>
                    <input type="text" name="user_name" id="name" autocomplete="off" onchange="user_validate('user_name', this.value);" />
                </li>
                <li>
                	<label>EMAIL:</label>
                    <input type="text" name="user_email" autocomplete="off" onchange="email_validate('user_email', this.value);"/>
                </li>
                <li>
                	<label>PASSWORD:</label>
                	<input type="text" name="user_pass" autocomplete="off" onchange="pass_validate('user_pass', this.value);" />
                </li>
            </ol>
            <fieldset>
            	<input type="submit"  value="Submit" name="submit" onclick="reg_submit()" />
				<div id="submit_reply"></div>
            </fieldset>
        </fieldset>
    </form>

HTML:

function reg_submit(){
	
	var submit = document.getElementById('submit_reply');
	
	var field_name = document.getElementById('name');
			
	var field_value = field_name.value;
	
	if(field_name) {
		
		params = "?" + field_name + "=" + field_value;
		
	}
	
	ajaxRequest.open("GET", "register.php" + params, true);
	
	ajaxRequest.onreadystatechange = function () {
		
		if(ajaxRequest.readyState == 4 && ajaxRequest.status == 200) {
			
			submit.innerHTML = ajaxRequest.responseText;
			
		} 
		
	}
	
	ajaxRequest.send(null);
		
}

Code (markup):

if(isset($_GET['submit'])){
	
	echo 'Form has been submitted';
	
}

PHP: