There are multiple logical design errors in the flow of your program. One of them is that you assign an arrayref to $hoa{$key} while you want it to be an arrayref itself, so you have to push your data in that array like push @{hoa{$key}}, [ @aoa ]. This assignment is also misplaced, as it will push an empty arrayref in case the line from <DATA> doesn't match any of the pattern you mentionned (/^\s+/ won't match an empty line by the way, /^$/ will).

Here's some code that will produce what you want. You may look at that solution (among others, as always) directly, or try and correct your code a bit by yourself first.

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;

my $key;
my %hoa;

while ( <DATA> )
{
   chomp;
   next if (/^$/);

   if ( /^SET/ )
   {
     $key = (split)[1]; # perldoc -f split
   }
   elsif (/^\d/)
   {
       push @{$hoa{$key}}, [ split /,/ ]; # perldoc -f split
   }

}
       print Dumper \%hoa ;

__DATA__
SET: SET1

0,100,BOOK
1,150,PENCIL
====

SET: SET2

2,110,ERASER
2,200,PEN
0,220,BLACKBOARD
1,300,CHALK
====
[download]

Update: updated explanations a bit, small updates to the code.