Wouldn't the mode value come from CGI then? Make sure you set a default run mode or the 'rm' parameter is present in the request. There should be detailed instructions in the CGI::Application perldoc. Wish you luck!

Here's link to a tutorial that might help. Although, from a quick glance at your code, you seem to have done things right. Still, may be worth checking over. One immediate suggestion might be to try setting run mode parameter and default value after the code which defines all run modes:

sub setup { 
  my $self = shift; 
  $self->run_modes( 
    'mode1' => 'Login', 
    'mode2' => 'DPR_Dashboard', 
    'mode3' => 'EnterPrsRls', 
    'mode4' => 'ApprovePrsRls', 
    'mode5' => 'ChooseLists', 
    'mode6' => 'ScheduleDistro', 
    'mode7' => 'AuthorizeDistro', 
    'mode8' => 'ReviewJobs' ); 

    $self->start_mode('mode1'); 
    $self->mode_param('rm'); 

  return 1; 
}