I'm sure you need to use `$mech->submit_form()` with `button` param.

$mech->submit_form(
 with_fields => {
  login_field => "somelogin",
  password_field => "somepassword",
 },
 button => "your_submit_button_name",
);
[download]

But may be some JavaScript magic is used by this webpage so you need to check headers submitted from your web browser (I use Firefox's HTTPFox add-on for this). Also there is no need to

$mech->cookie_jar(HTTP::Cookies->new());
[download]

because Mechanize will work with cookies by default...