Why Not Convert HTML to XML?
Just to play devil's advocate for a minute, it seems like HTML is just too darned close to XML to have to parse this way. Isn't there a library out there for converting HTML into XHTML? If you can do that, you can just read the file in using XmlDocument::LoadXml(). Once you've done that, you can find your tags using an XPath query. Sorry, I just couldn't let a parsing post go by without tossing in my two cents ;)
In fact, there are two approaches to this. The first recognizes that HTML is really just a subset of SGML. Thus if you have a SGML parser, you're done. So one option is to try Chris Lovett's SgmlReader.
In fact, this is what the current version of RSS Bandit uses for auto-discovery of RSS feeds within HTML content. However, I recently replaced it with regular expressions because of some memory use and performance problems we were having with it. In our case, finding these tags is a lot faster and uses less memory by just using a regular expression. (Now you see the motivation for the post).
Another option is to use Simon Mourier's HTML Agility Pack. He takes an interesting approach in that he provides an HtmlDocument class that implements System.Xml.XPath.IXPathNavigable. Thus his approach provides the same interface as an XmlDocument for querying nodes, but doesn't change the underlying HTML content as many other approaches would by converting them to XML.
And just to toot Pat's horn a bit, I used to be his manager at Solien when he was just starting out in his career. Now he works at Univision and has inherited reams of code that parse through Fortran code as well as proprietary database files. He's also written his own grammar engine and xml syntax for describing computer languages such as C#. So he knows a thing or two about parsing text. He's become quite a top notch developer. I'm just waiting for him to get off his arse and start a blog.