You should select the form first to work on after the get() method. Saying $mechObject->form_number(1) means that work on the form number 1, which is the only form in the HTML. The field() method works on a single field, so you have to call it twice for to fill in two fields. The click() method returns HTTP::Response object so you may interested the clicking result or the content returned by the server.

my $resp = $mechObject->click;
die "Submit failed\n" if $resp->is_error;
my $content = $resp->content;
# do something with $content if necessary
[download]

However, if you have problem due the the JavaScript in the HTML source, check mechanize and javascript.