Basically the same answer, but a little more golfed:

use strict;
use Data::Dumper;

my %data;
my $current_key;

while( <DATA> ) {
    my ($key, $value) = m[^((?:\w{2})?)\s+(.*)] or die "Bad line: $_";
    last if $key eq 'ER';
    $current_key = $key || $current_key;
    die "No key defined" unless $current_key;
    push @{ $data{$current_key} }, $value;
}

print Dumper \%data
__DATA__
T1 Line1
T2 Line2
   Line3
   Line4
T3 Line5
   Line6
ER
[download]

Updated. I should test these things first :-) (and its silly that (\w{2}?) doesn't DWIM) (and see Aristotle's answer further down for a very similar answer). Oh well).