The problem is, of course, that you're not sending the same header/data as FireFox does. There is no magic solution by which we can tell you in what way the data your script sends differs from the data your browser sends.

You will need to analyze the differences between the data - maybe it is already enough to use WWW::Mechanize instead of raw LWP, as WWW::Mechanize provides behaviour close to browsers, but maybe it isn't. You have to look at the differences.

The Ethereal approach is the right direction - I've written myself Sniffer::HTTP to automate the sniffing of HTTP headers, and HTTP::Request::FromTemplate to regenerate requests from text files.