C:\Users\Bill\forums\monks>type 1203224.pl
use strict;
use warnings;
my $output = <<'END_OUT';
PEM 0:

PEM 1:

PEM 2:
  State:     Online

PEM 3:
  State:     Online

END_OUT

while ($output =~ m/^(PEM\s\d) \: $ \n ^ \s\sState: [ ]+ (Online)$/xmg) {
    print "$1 $2\n";
}

C:\Users\Bill\forums\monks>perl 1203224.pl
PEM 2 Online
PEM 3 Online