A couple of things. You need to pass the live CGI query to the subs at runtime, and you want to use the $username value you pass to set_cookie:

sub set_cookie {
    my ( $q, $username) = @_;
    my $cookie = $q->cookie ( name   =>    "login",
                              value  =>    $username,
                              path   =>    "/cgi-bin");
                                  
    print $q->redirect( -url => "http://www.foo.com/cgi-bin/bar/index.
+cgi?page=logedin",
                        -cookie => $cookie );
}
[download]

with corresponding changes in sub logedin{} and the calls.

After Compline,
Zaxo