You may want to try checking permissions. Also check linefeeds of you're moving the file back and forth between Windows and Unix (some ftp clients don't convert them). I just copied both of your code snippets into two separate files and hit it with my browser and it worked. I added some parameters to the query string, and got the outputPost data printing too.

test.cgi:

#!/usr/bin/perl -w

use strict;
use CGI;
use CGI::Carp qw(fatalsToBrowser);

require "functions.pl";

# define a hash to contain any "global" objects or variables
our %GLOBAL = (
  'query' => '',
    'test' => 'foobar!'
    );

$GLOBAL{'query'} = new CGI;

print CGI::header();
outputTest();
outputPOST();
[download]

functions.pl:

sub outputTest
{
          print $main::GLOBAL{'test'};
}

sub outputPOST
{
          print $main::GLOBAL{'query'}->Vars;
}

1;
[download]

Hit the browser with http://192.168.1.102/test/test.cgi:

foobar!
[download]

Hit the browser with http://192.168.1.102/test/test.cgi?myvar=haha:

foobar!myvarhaha
[download]