This is what I have. Hope it makes sense! Since your hash has an array as the value, you just have to tell perl to check what specific thing you want to look at.

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

#seting up your things
#$barcode_hash{$prim_pair_number} = [ $fowprim, $revprim, $bc_pair, $b
+c_pair_num ];
my %VAR1 = (
        '1' => [
                'AGCTCGTTGTTCGATCCA',
                'GAGAGATAGATGATAGTG',
                'TTTT_CCCC',
                 0
                 ],
         '2' => [
                 'AGCTCGTTGTTCGATCCA',
                 'GAGAGATAGATGATAGTG',
                 'TTTT_AAAA',
                  0
                 ]
             );
my $barcode_pair_35 = 'TTTT_CCCC';


#for each key in the hash, if the 3rd element (i.e. index 2) is equal 
+to $barcode_pair_35,
#then incriment the 4th element (i.e. index 3) and print that you foun
+d it.
foreach my $prim_pair_num (sort keys %VAR1){
        if($VAR1{$prim_pair_num}[2] eq $barcode_pair_35){
                $VAR1{$prim_pair_num}[3]++;print "found it\n";print $V
+AR1{$prim_pair_num}[3]."\n";
        }#endof if

}
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