From the tutorial you linked, the relavent code is:

sub setup { 
    my $self = shift; 
    $self->start_mode('mode1'); 
    $self->run_modes( 
       'mode1' => 'helloworld_cgi_app1', 
       'mode2' => 'helloworld_cgi_app2', 
       'mode3' => 'helloworld_cgi_app3', 
       ); 
}
[download]

The error comes because 'mode1' is not defined in your setup function - the hash passed to run_modes sets up the "Oh, I got the run mode parameter 'mode1'; which function do I call now?" part of CGI::Application. I don't see off the top of my head why cutting and pasting wouldn't work, so if you could show us your code, that would help. :-)