As a general solution to any HTML-parsing problem, I've had good success with HTML::TreeBuilder. Once you get the response object back (I assume you're using LWP or WWW::Mechanize), you can elementify it and then step through the resulting tree, looking for your code or content with the as_HTML() or as_text() methods (HTML::Element).

I never really got TreeBuilder working well when dealing with nested tables, but that may have been more a lack of diligence on my part than any particular deficiency in TreeBuilder or HTML::Parser.