Problems with your code:

• Cookies and URL parameters are two really different things. Simply passing a cookie as URL parameter usually does not work, simply because (on a properly coded server) cookies, URL parameters and POSTed parameters are three completely independant name spaces. There are commercial server systems where this is not the case, but they are rare and usually not available from the internet.
• WWW::Mechanize and your IE will probably send very different HTTP headers, even when you tell W::M to identify as IE 6. A sufficiently paranoid server will detect this and refuse to accept the faked IE session.
• I see no tests after $mech->submit() that the login really worked.

Alexander