Greetings,
Try sorting it twice.

#!/usr/bin/perl  -w
use strict;

my @array = ();

while (<DATA>){
    chomp($_);
    my @subarray = split(/,/,$_);
    push @array, [@subarray];
}

my @sorted = 
    sort { $a->[1] <=> $b->[0] } #by parent
    sort { $a->[0] <=> $b->[0] } #by id
    @array;

for my $x(0..$#sorted){
    print "$sorted[$x][0]:$sorted[$x][1] - $sorted[$x][3]\n";
}

#id,parent,stamp,text
__DATA__
1,0,2006-01-02 08:15:00,test line 1 (first)
2,1,2006-01-02 08:16:00,test line 2 (second)
3,2,2006-01-02 08:21:00,test line 3 (third)
6,1,2006-01-02 08:23:00,test line 6 (seventh)
4,1,2006-01-02 08:22:00,test line 4 (sixth)
7,6,2006-01-02 08:25:00,test line 7 (eighth)
5,3,2006-01-02 08:23:00,test line 5 (fourth)
8,1,2006-01-02 08:17:00,test line 8 (fifth)
[download]

The output

#id:parent - text

1:0 - test line 1 (first)
2:1 - test line 2 (second)
3:2 - test line 3 (third)
5:3 - test line 5 (fourth)
4:1 - test line 4 (sixth)
6:1 - test line 6 (seventh)
7:6 - test line 7 (eighth)
8:1 - test line 8 (fifth)
[download]

Perhaps Im missing something (which is always possible) but Im not sure how id:8, parent:1 was going to end up fifth???
Is that close to what you were looking for?

-InjunJoel