There the <script> is for. Just initially hide the particular piece using CSS and use JavaScript to display it. Here's a basic kickoff example:
<!doctype html>
<html lang="en">
<head>
<title>SO question 2297643</title>
<script>
window.onload = function() {
document.getElementById("foo").style.display = 'block';
};
</script>
<style>
#foo { display: none; }
</style>
</head>
<body>
<noscript><p>JavaScript is disabled</noscript>
<div id="foo"><p>JavaScript is enabled</div>
</body>
</html>
...or, with little help of jQuery ready() which is a tad sooner with displaying the content:
<!doctype html>
<html lang="en">
<head>
<title>SO question 2297643 with jQuery</title>
<script src="http://code.jquery.com/jquery-latest.min.js"></script>
<script>
$(document).ready(function() {
$('#foo').show();
});
</script>
<style>
#foo { display: none; }
</style>
</head>
<body>
<noscript><p>JavaScript is disabled</noscript>
<div id="foo"><p>JavaScript is enabled</div>
</body>
</html>
To improve user experience, consider placing the <script> call directly after the particular HTML element which needs to be toggled, so that there's no "flash of content" or "element shuffle". Andrew Moore has given a good example in this topic.
Alternatively, you can do it (hacky) the other way round with <style> in <noscript>. This is syntactically invalid, but allowed by all browsers from IE6 and up, including the W3C-strict Opera:
<!doctype html>
<html lang="en">
<head>
<title>SO question 2297643 with CSS in noscript</title>
</head>
<body>
<noscript>
<style>#foo { display: none; }</style>
<p>JavaScript is disabled
</noscript>
<div id="foo"><p>JavaScript is enabled</div>
</body>
</html>
