There's gotta be like tens of different ways to achieve that, i ll give you two;

1.Open all links in new windows in entire linkblog;

<?php
If  ($Blog->ID ==1){
// "1" being ID of your linkblog
?>
    <script>$('a[href^="http://"]')
  .attr("target", "_blank");</script>
<?php } ?>

2.Open only linkblog links in new window, and keep the sidebar, header etc links as is.

Assuming linkblog itself is a widget, it should be able to have its very own widget class, even if it doesnt, you can still use the class or id of the div that you have inserted your linkblog widget into.(ex: #content)

<script type="text/javascript">       
        $(".linkblog_widget_class").click(function() {   
            strUrl=$(this).find("a").attr("href");       
            window.open(strUrl);return false;         
        });       
    });</script>

Obviously those above are jquery hacks, so, needless to say, you will need to load jquery first, and put these hacks into your body.footer.inc.php right before the last closing tag