You haven't printed out the strings you're trying to compare:

   $_ = "Priority Kirkgate, PC7588\n";
   @fields = split /,/, $_ ;
   print "PC string from NEW list: >>$fields[1]<<";
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This code will have your PC code with a leading space, and the rest of your code won't match that.

Also, it's not really efficient to read through the $old_file for every comparison. I'd read new computers into a hash and then check while stepping through $old_file whether the computer is known or not:

use strict;
my %new_pc;

...

while (<IN1>) {
   chomp;
   $count_in++;
   @fields = split /,/, $_;
   $PC_NO  = $fields[1];
   $PC_NO =~ s/\s*//g;
   $new_pc{ $PC_NO } = 1;
};

...

while (<IN2>) {
   chomp;
   if (/CN=(PC\d+)\.OU/) {
       my $pc = $1;
       if (exists $new_pc{ $pc }) {
           # $pc is old and new, hence has survived
           delete $new_pc{ $pc };
       } else {
           # $pc is old but not new, hence has been removed
       };
   } else {
      warn "Ignoring line >>$_<<";
   };
};

# All PCs in %new are now really new:
for my $pc (keys %new) {
    print "$pc is new\n";
};
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