Add this to your function.php

function my_custom_dashboard_text() {

echo '<h2>Open A New Support Ticket</h2>

<p>Use this form to report bugs, problems, requests for upgrades, modifications, additions and other support issues directly to (support team). Note that grades will be sent email response associated to your profile (user@domain.com).</p>

	<form action="http://helpdesk.domain.com/open.php" method="post" enctype="multipart/form-data" id="technical-support-form">
		<fieldset id="form-name" class="Required">
			<label>Name:</label>
			<input type="text" name="name" value="" />
<BR>
		</fieldset>
		<fieldset id="form-email" class="Required">
			<label>Email:</label>
			<input type="text" name="email" value="" />
			<BR>
		</fieldset>
		<fieldset >
			<label>Phone:</label>
			<input type="text" name="phone" value="" />
		</fieldset>
		<fieldset id="form-topic" class="Required">
			<label>Topic:</label>
			<select name="topicId">
				<option value="" >Select</option>
				<BR>
				<option value="0" >General Inquiry</option>
<option value="1" >Support</option>
			</select>
			</fieldset>
		<fieldset id="form-subject" class="Required">
			<label>Subject:</label>
			<input type="text" name="subject" value="" />
			</fieldset>
		<fieldset id="form-message" class="Required">
			<label>message:</label>
			<textarea rows="5" cols="80" name="message"></textarea>
			</fieldset>
<?}?>
		<fieldset id="button-group">
			<input class="FormButton" type="submit" name="submit_x" value="Submit" />
			<input class="FormButton" type="reset" value="Reset" />
			<input class="FormButton" type="button" name="cancel" value="Cancel"/>
		</fieldset>
	</form>';
}function my_custom_dashboard_widgets() {
wp_add_dashboard_widget('custom_text_widget', 'Support tickets', 'my_custom_dashboard_text');
}

add_action('wp_dashboard_setup', 'my_custom_dashboard_widgets');

This code will add a new widget on wordpress dashboard.

I need help here to make it work as a plugin or to be able to make it popup with js script after submitting the ticket.

I am no php expert or js and i made this code from several threads here.

Any help will be blessing :)