I spent about entire day trying to solve this problem. I couldn't manage to display "BROWSE SERVER" button in FCKeditor. It only occured when IMCE is enabled. When I disable IMCE and let FCKeditor manage uploads it all works perfectly.
I used garland template as a base for my custom template. That's why I was so puzzled why it would not work. And finally few minutes ago I managed to find where it is.
This is the code that was causing the issue:
<script type="text/javascript">
<!--
SET_DHTML("admin_menu_navigation","block-user-1");
//-->
</script>
<?php print $closure ?></body>
</html>
I had to remove everything that is above print $closure.
This of course means that I have to figure out what to do with this piece of JS code. But IMCE is more important at this point. Just thought this might be useful info for someone in the future stumbling upon the same.