You didn't mention this, but if order matters in some way, you would might want two data structures, one to unique the output (a hash) and one to maintain ordering (an array). I don't know if you have seen this with the previous examples, but the header line could get mixed into the file somewhere (randomly, thanks to the hashing algorithm) unless handled separately. Alternatively, I provide this quick example:

#!/usr/bin/perl

use strict;
use warnings;

my @order; my %data;

while (<DATA>) {
    my ($key,$value) = split /\t/, $_, 2;
    push @order, $key;
    $data{$key} = $value;
}

for my $key (@order) {
    printf("%s\t%s", $key, delete $data{$key}) if ($data{$key});
}

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