When I write these web automation things, the first step is to be able to get the HTML of the page I want. You can save the resulting HTML from LWP/Mechanize as a file and then open that file in Firefox to make sure you're getting correct stuff that is the same as when you use the browser to go there. Have you passed this hurdle yet?

Then the question becomes: How do I get what I want out of this HTML? That is an application specific thing. If it is really easy, I just write a regex. HTML Parser is one option.