This is an easy problem to solve (and you can sort multiple ways with the same code) if you will use a hash (I'll note the link shows yet another way to do this kind of operation).

#!/usr/bin/perl
use warnings;
use strict;
use Getopt::Long;
use Pod::Usage;

 =head1 NAME

 unique.pl -- examines data and keeps the unique ones. 

 =head1 SYNOPSIS

 unique.pl [options]
 Options:
        --help          Brief help message
        --man           Full documentation
        --first         Keep the first one found rather than the last.

 =head1 DESCRIPTION

 unique.pl -- examines data and keeps the unique ones. 
 Program can keep the first or the last one found.

 =cut

my $help    = 0;
my $man     = 0;
my $first   = 0;

GetOptions(
    'help|?'    => \$help,
    man         => \$man,
    first    => \$first,
) or pod2usage(2);

pod2usage( -exitval => 0, -verbose => 1 ) if $help;
pod2usage( -exitval => 0, -verbose => 2, -noperldoc => 1 ) if $man;

my %hash = ();
while(<DATA>) {
    chomp;
    my ( $comp, $id, $status ) = split ( /\s+/, $_, 3 );
    next if ( $comp =~ m/COMPUTER/ );
    if ( $first ) {
        next if ( defined( $hash{$comp} ) );
    }
    $hash{$comp} = [ $id, $status ];
}
for ( sort keys %hash ) {
    printf "%s %s %s\n", $_, $hash{$_}->[0], $hash{$_}->[1];
}

__DATA__
COMPUTER      DISTRIBUTION_ID    STATUS    
30F-WKS     `1781183799.xxxx1'      IC---
30F-WKS     `1781183799.xxx11'      IC---
ADM34A3F9   `1781183799.41455'      IC---
[download]

and the results are:

C:\Code>perl unique.pl --help
Usage:
     unique.pl [options]
     Options:
            --help          Brief help message
            --man           Full documentation
            --first         Keep the first one found rather than the l
+ast.


C:\Code>perl unique.pl
30F-WKS `1781183799.xxx11' IC---
ADM34A3F9 `1781183799.41455' IC---

C:\Code>perl unique.pl --first
30F-WKS `1781183799.xxxx1' IC---
ADM34A3F9 `1781183799.41455' IC---
[download]