#!/usr/bin/perl
use strict;
use warnings;

local $/="}"; # So we can slurp an entire service in one read
my $host_txt= "host_name";
my $check = "check_nrpe";
my $con = "contact_groups";

while (my $list = <DATA>){
    next if $list=~/PING/; # UPDATE: O.P. Added this sample after I po
+sted
    next unless $list=~ m/$host_txt\s+(\w+).+$check.+$con\s+(\w+)/so;
    print "GROUP NAME: $2; for host $1\n";
}

__DATA__
define service {
       host_name                       KT
       service_description             Check SSH
       check_command                   check_ssh
       max_check_attempts              1
       check_interval                  1
       retry_interval                  2
       check_period                    24x7
       check_freshness                 1
       contact_groups                  admins
       notification_interval           60
       notification_period             24x7
       notifications_enabled           1
       register                        1
 }
 
 define service {
      host_name                       KT
      service_description             Controller Load
      check_command                   check_nrpe!check_load
      max_check_attempts              1
      check_interval                  1
      retry_interval                  2
      check_period                    24x7
      check_freshness                 1
      contact_groups                  admins
      notification_interval           60
      notification_period             24x7
      notifications_enabled           1
      register                        1
 }
[download]

GROUP NAME: admins; for host KT
[download]

.. if I use the || instead of &&, the output I get contains contact_group output from PING ...

This doesn't seem possible to me: given the code you posted, no @input line with a 'PING' substring will be processed further. The && (logical and) of regex matches works for me as I expect:

c:\@Work\Perl\monks>perl -wMstrict -le
"my @input = (
   'PING foo wrong',
   'PING check_nrpe wrong',
   'PING contact_groups wrong',
   'PING check_nrpe contact_groups wrong',
   'PING contact_groups check_nrpe wrong',
   'foo wrong',
   'check_nrpe wrong',
   'contact_groups wrong',
   'check_nrpe contact_groups BINGO!',
   'contact_groups check_nrpe BINGO!',
   );
 ;;
 my $check = 'check_nrpe';
 my $con   = 'contact_groups';
 ;;
 for my $list (@input) {
   next if $list =~ /PING/;
   ;;
   print qq{'$list'} if $list =~ /$check/ && $list =~ /$con/;
   }
"
'check_nrpe contact_groups BINGO!'
'contact_groups check_nrpe BINGO!'
[download]

Update: Be aware that you are processing the example file on a line-by-line basis (update: with the code you've posted), not on a  define service { ... } block basis.

if ($list =~ /$check/ && $list =~ /$con/) {

This condition will never be true because there is no line in your input file which matches both regular expressions.

Depends on how you define 'line', and regex options used. See my (working) solution above.

                As a computer, I find your faith in technology amusing.

Here's another guess at what you might want. Uses OPed example input file and hard-coded file name. Warning: Not extensively tested. (This runs under Perl version 5.8.9.)

File edit_nagios_cfg_2.pl: