First, let's change our new themesidebox2 function to create ONLY a simple empty frame:

function themesidebox2($title, $content) {
    global $bgcolor1;
    echo "<table border="0" cellspacing="0" cellpadding="0" width="150">"
        ."<tr><td bgcolor="$bgcolor1">"
        ."$content"
	."</td></tr></table><br>";
}

Save the file to your site, and test. (make sure you have selected the right theme in Your Account!)

You should now have a modules block that has no title and no box frame.
There will just be links floating there on the site's default background color.