first of all. are your sure a client-side solution using javascript isn't sufficent to your needs?
because the easiest way to count nodes within an HTML document is using jQuery on the client-side browser.
<script src="http://code.jquery.com/jquery-1.7.min.js"></script>
<script>
$('html').children() // will give you all child elements of the html element
$('body').children() // same for body element
$('body').children('div') // will give you just the direct children elements of 'div' type
$('body').find('div') // will give you all the nested elements of 'div' type
</script>
if you are unfamilier with jQuery then take a look at www.jquery.com
if u still need a C# solution for server-side parsing of the document then then i would recommend to use HTMLAgilityPack (even thou you wish not to). writing your own parser seems to me like a waste of time as you need to consider malformed html/xml and such which can be a pain.
try and use this s-overflow article: What is the best way to parse html in C#?
hope it will satisfy your needs