With the same principle as brother Veltro, here is a take with some tests (whose number you can happily expand to your satisfaction). It uses Text::CSV_XS and thus allows for less strictly-formed inputs, should they arise. The final output of the normalised dataset is left as a simple exercise.

#!/usr/bin/env perl 
use strict;
use warnings;
use Test::More tests => 3;
use Text::CSV_XS;

my $csv = Text::CSV_XS->new;
my %out;
while (my $colref = $csv->getline (*DATA)) {
    next if exists $out{$colref->[0]};
    $out{$colref->[0]} = [@$colref[1,3,4,5]];
}

is (scalar (keys %out), 19, 'Have correct number of output lines');
is_deeply ($out{key_683}, ['march', 'ABCD_FH', 9, 9], 'First line is g
+ood');
is_deeply ($out{key_701}, ['march', 'ABC_H + AB_F', 2, 19], 'Last line
+ is good');

__DATA__
key_683,march,29031990,ABCD_FH,9,9
key_684,march,29031990,ABCD_FH,9,9
key_685,march,29031990,ABCD_FH,9,9
key_686,march,29031990,ABCD_FH,9,9
key_687,march,29031990,ABCD_FH,9,9
key_688,march,29031990,ABCD_FH,9,9
key_689,march,29031990,ABCD_FH,9,9
key_693,march,29031990,ABCD_FH,9,9
key_694,march,29031990,ABCD_FH,9,9
key_683,march,29031990,ABCD_H + ABC_F,8,17
key_684,march,29031990,ABCD_H + ABC_F,8,17
key_685,march,29031990,ABCD_H + ABC_F,8,17
key_686,march,29031990,ABCD_H + ABC_F,8,17
key_687,march,29031990,ABCD_H + ABC_F,8,17
key_688,march,29031990,ABCD_H + ABC_F,8,17
key_689,march,29031990,ABCD_H + ABC_F,8,17
key_690,march,29031990,ABCD_H + ABC_F,8,17
key_691,march,29031990,ABCD_H + ABC_F,8,17
key_692,march,29031990,ABCD_H + ABC_F,8,17
key_693,march,29031990,ABCD_H + ABC_F,8,17
key_694,march,29031990,ABCD_H + ABC_F,8,17
key_695,march,29031990,ABCD_H + ABC_F,8,17
key_696,march,29031990,ABCD_H + ABC_F,8,17
key_697,march,29031990,ABCD_H + ABC_F,8,17
key_698,march,29031990,ABCD_H + ABC_F,8,17
key_699,march,29031990,ABCD_H + ABC_F,8,17
key_683,march,29031990,ABC_H + AB_F,2,19
key_684,march,29031990,ABC_H + AB_F,2,19
key_685,march,29031990,ABC_H + AB_F,2,19
key_686,march,29031990,ABC_H + AB_F,2,19
key_687,march,29031990,ABC_H + AB_F,2,19
key_688,march,29031990,ABC_H + AB_F,2,19
key_689,march,29031990,ABC_H + AB_F,2,19
key_690,march,29031990,ABC_H + AB_F,2,19
key_691,march,29031990,ABC_H + AB_F,2,19
key_692,march,29031990,ABC_H + AB_F,2,19
key_693,march,29031990,ABC_H + AB_F,2,19
key_694,march,29031990,ABC_H + AB_F,2,19
key_695,march,29031990,ABC_H + AB_F,2,19
key_696,march,29031990,ABC_H + AB_F,2,19
key_697,march,29031990,ABC_H + AB_F,2,19
key_698,march,29031990,ABC_H + AB_F,2,19
key_699,march,29031990,ABC_H + AB_F,2,19
key_700,march,29031990,ABC_H + AB_F,2,19
key_701,march,29031990,ABC_H + AB_F,2,19
[download]

I created this for you so you have something you can start playing with. I think it already does what you want. It works by creating a hash with keys and it depends on the fact that a hash key has to be unique and you can use 'exists' to see if the key already exists.

use strict ;
use warnings ;

while(<DATA>) {
    chomp ;
    my @values = split(',', $_) ;
    # print "values = @values\n" ;
    processKey( @values ) ;
}

my $foundKeys = {} ;

sub processKey {
    my $key = $_[0] ;
    my $col2 = $_[1] ;
    my $col3 = $_[2] ;
    my $col4 = $_[3] ;
    my $col5 = $_[4] ;
    my $col6 = $_[5] ;
    
    if ( exists $foundKeys->{ $key } ) {
        # skip
    } else {
        $foundKeys->{ $key } = 1 ;
        print "$key $col2 $col3 $col4 $col5 $col6\n" ;
    }
}

__DATA__
key_683,march,29031990,ABCD_FH,9,9
key_684,march,29031990,ABCD_FH,9,9
key_685,march,29031990,ABCD_FH,9,9
key_686,march,29031990,ABCD_FH,9,9
key_687,march,29031990,ABCD_FH,9,9
key_688,march,29031990,ABCD_FH,9,9
key_689,march,29031990,ABCD_FH,9,9
key_693,march,29031990,ABCD_FH,9,9
key_694,march,29031990,ABCD_FH,9,9
key_683,march,29031990,ABCD_H + ABC_F,8,17
key_684,march,29031990,ABCD_H + ABC_F,8,17
key_685,march,29031990,ABCD_H + ABC_F,8,17
key_686,march,29031990,ABCD_H + ABC_F,8,17
key_687,march,29031990,ABCD_H + ABC_F,8,17
key_688,march,29031990,ABCD_H + ABC_F,8,17
key_689,march,29031990,ABCD_H + ABC_F,8,17
key_690,march,29031990,ABCD_H + ABC_F,8,17
key_691,march,29031990,ABCD_H + ABC_F,8,17
key_692,march,29031990,ABCD_H + ABC_F,8,17
key_693,march,29031990,ABCD_H + ABC_F,8,17
key_694,march,29031990,ABCD_H + ABC_F,8,17
key_695,march,29031990,ABCD_H + ABC_F,8,17
key_696,march,29031990,ABCD_H + ABC_F,8,17
key_697,march,29031990,ABCD_H + ABC_F,8,17
key_698,march,29031990,ABCD_H + ABC_F,8,17
key_699,march,29031990,ABCD_H + ABC_F,8,17
key_683,march,29031990,ABC_H + AB_F,2,19
key_684,march,29031990,ABC_H + AB_F,2,19
key_685,march,29031990,ABC_H + AB_F,2,19
key_686,march,29031990,ABC_H + AB_F,2,19
key_687,march,29031990,ABC_H + AB_F,2,19
key_688,march,29031990,ABC_H + AB_F,2,19
key_689,march,29031990,ABC_H + AB_F,2,19
key_690,march,29031990,ABC_H + AB_F,2,19
key_691,march,29031990,ABC_H + AB_F,2,19
key_692,march,29031990,ABC_H + AB_F,2,19
key_693,march,29031990,ABC_H + AB_F,2,19
key_694,march,29031990,ABC_H + AB_F,2,19
key_695,march,29031990,ABC_H + AB_F,2,19
key_696,march,29031990,ABC_H + AB_F,2,19
key_697,march,29031990,ABC_H + AB_F,2,19
key_698,march,29031990,ABC_H + AB_F,2,19
key_699,march,29031990,ABC_H + AB_F,2,19
key_700,march,29031990,ABC_H + AB_F,2,19
key_701,march,29031990,ABC_H + AB_F,2,19
[download]

This terse approach may hint at future possibilities for text file hackery:

perl -M5.010 -Mstrict -F, -wanle '
    BEGIN{ $" = "," }
    our ($rpt, $non_key);
    if ( ($non_key // "") eq "@F[1..5]"){
        print; # this line not right - exercise left to reader
    }
    else {
        $rpt = $F[4] -1;
        $non_key = "@F[1..5]";
        print
    }
'
[download]