I believe Yahoo checks for a cookie and then lets you in. If so, you might have a look at LWP::UserAgent and HTTP::Cookies.

Even better, you can do this (from the docs):

$cookie_jar = HTTP::Cookies::Netscape->new(
    File     => "$ENV{HOME}/.netscape/cookies",
    AutoSave => 1,
);
[download]

That'll give your cookie jar access to existing Netscape cookies. From there, you can save them to another file, clear the Netscape cookie, and be in business. (Though how this will work without your program acting as a proxy server of some sort is beyond me.)