Limiting conditional comment to home only in header.php

There are likely more elegant ways to do this sort of thing, but the quickest and easiest, using your code, would be to move the PHP conditional out of the CSS conditional. e.g. change this:

<!--[if lt IE 9]><?php if(is_home() )?> 
    <script type="text/javascript" src="https://wordpress.stackexchange.com/questions/27299/<?php bloginfo("template_url'); ?>/scripts/unitpngfix.js"></script>

…to this:

<?php if( is_home() ) { ?> 
<!--[if lt IE 9]>
    <script type="text/javascript" src="https://wordpress.stackexchange.com/questions/27299/<?php bloginfo("template_url'); ?>/scripts/unitpngfix.js"></script>
<?php } ?>

Also: aren’t you missing the closing of the CSS conditional here?

<?php if( is_home() ) { ?> 
    <!--[if lt IE 9]>
    <script type="text/javascript" src="https://wordpress.stackexchange.com/questions/27299/<?php bloginfo("template_url'); ?>/scripts/unitpngfix.js"></script>
    -->
<?php } ?>