After update to 4.4.4. notification on new chat messages works, but user that has no messages cannot get to Chat section since there is no Show All button like Notifications and Friends have. If no messages are present on profile notification displays ajax-loader.gif indefinitely and no Show All button is present. Also, Show All button should be present even when there are conversations in Chat present.
Only way to access Chat page is to right click on envelope icon and open link in new tab when you get :

This is your inbox
Conversations will start showing here once you have your first chat with someone. You can start a conversation with your friends any time.
Please add some friends before you can make new conversations.

This is valid but, thank you reporting..

As far as I can see there are 2 problems:
1) infinite loader.gif that is not replaced with some text as notification that there are no conversations
2) no Show All button as way to quickly access Chat/Messages page
Found how to display Show All button. Add at end of ...\components\com_community\templates\YOUR_THEME\layouts\chat\notification-item.php

<a class="joms-button--neutral joms-button--full" href="<?php echo CRoute::_('index.php?option=com_community&view=chat'); ?>">
    <?php echo JText::_('COM_COMMUNITY_NOTIFICATIONS_SHOW_ALL_MSG'); ?>
</a>

Please we wait the fix patch from our developer..

Hi,

To fix this open this file
modules/mod_community_bar/tmpl/default.php
modules/mod_community_hellome/tmpl/default.php
modules/mod_community_notifications/tmpl/default.php
on those file find this code

<img src="<?php echo JURI::root(true); ?>/components/com_community/assets/ajax-loader.gif" alt="loader">

<span><?php echo JText::_('COM_COMMUNITY_CHAT_NOTIF_NO_NEW_MESSAGE') ?></span>