витослав,
<!DOCTYPE HTML>
<html>
<head>
<title>Untitled</title>
<script>
function changeButtonState() {
var btn = document.getElementById('invisible');
btn.style.display=document.querySelectorAll(":checked").length ? 'block': 'none';
}
</script>
<style type="text/css">
#invisible {
display: none;
}
</style>
</head>
<body> <input id="invisible" name="" type="button" value="go">
<ul>
<li><input type="checkbox" name="check[]" onChange="changeButtonState()" value="123"> 123</li>
<li><input type="checkbox" name="check[]" onChange="changeButtonState()" value="123"> 123</li>
</ul>
</body>
</html>