You don't tell us which version of WWW::Mechanize you have installed. You could find out the version by running:

perl -MWWW::Mechanize -e "die WWW::Mechanize->VERSION"
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The most common cause for this is that you did not set the proper form in your script. I notice a commented out line

#$mech->form_id('form');
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Maybe using the correct form helps. Or maybe there is no form on your page. I think at least version 1.73 of WWW::Mechanize outputs a proper warning instead of crashing the program.