The crux of your problem is understanding how
your firewall/proxy works. You need to come to an
understanding of how your firewall authentication works,
then you can address how to deal with it in perl.
Exactly how does the login you
have to do to browse the web work? Does your web browser
have to have any proxy settings?
There are proxy methods in LWP::UserAgent to support
proxying and other methods for
HTTP authentication; either of those might
fit the bill depending on how your firewall