Fossi in te cambierei completamente approccio...

codice:
<!doctype html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Esempio</title>
<script type="text/javascript">
var bShown = false;

function docClick (oPssEvt) {
	var bChange = bShown, oEvt = oPssEvt || /* IE */ window.event;
	for (var oEl = oEvt.target; oEl; oEl = oEl.parentNode) {
		if (oEl.className === "finestrella") { bChange = false; }
		else if (oEl.id === "pulsante") { bChange = true; break; }
	}
	if (bChange) {
		for (var nIdx = 0, aEls = document.getElementsByClassName("finestrella"); nIdx < aEls.length; nIdx++) {
			aEls[nIdx].style.display = bShown ? "none" : "block";
		}
		bShown = !bShown;
	}
}
 
document.onclick = docClick;
 
</script>
<style type="text/css">
.finestrella {
	position: fixed;
	display: none;
	left: 0;
	top: 0;
	width: auto;
	height: auto;
}
 
#myDiv {
	width: 300px;
	height: 200px;
	left: 200px;
	top: 200px;
	background-color: #00ff00;
}
</style>
</head>
 
<body>
 
<div class="finestrella" id="myDiv">

Hello world!</p></div>
<div class="finestrella" style="background-color:#aaaaaa;">Another hello world!</div>
<div id="pulsante">Clicca qui</div>
</body>
</html>