Installation
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1. install com_shoutbox.zip   (component)

2. install mod_shoutbox.zip   (module)

3. Open the index.php from the template you are using. Add the next 2 lines above </head>

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<link rel="stylesheet" href="<?php echo $mosConfig_live_site;?>/modules/mod_shoutbox_css.php" type="text/css" />
<script type="text/javascript" src="<?php echo $mosConfig_live_site;?>/modules/fatAjax.php"></script> 
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So it looks like this:

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<link rel="stylesheet" href="<?php echo $mosConfig_live_site;?>/modules/mod_shoutbox_css.php" type="text/css" />
<script type="text/javascript" src="<?php echo $mosConfig_live_site;?>/modules/fatAjax.php"></script> 
</head>
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4. Publish the module

no problem