Thank you. I actually was getting ready to post my final solution. I used a cpan module that included the exact operation I was looking for.

#!/usr/bin/perl -w
use strict;
use Array::Utils qw(:all);

my $boxEnd;
my $pathToDirectory;
my $pathToDatabase = "\\\\SHARESERVER\\DigiOfficeShare\\PerlDev\\Datab
+ase.txt";
my @contentsOfDataBase;
my @contentsOfDirectory;

print "First Box?", "\n";
chomp (my $boxBegining = <>);
print "Last Box?", "\n";
chomp ($boxEnd = <>);
print "\n", "Wait a minute while I look... Lazy...", "\n";

open my $databaseOutput, $pathToDatabase || die "\n", "Cannot find fil
+e.", "\n";
@contentsOfDataBase = <$databaseOutput>;
chomp @contentsOfDataBase;
close $databaseOutput;

while ($boxEnd >= $boxBegining) {
  my $pathToDirectory = "\\\\SHARESERVER\\DigiOfficeShare\\PerlDev\\Bo
+x $boxBegining";
  $boxBegining++;
  opendir(my $currentDirectory, $pathToDirectory) || die "\n", "You su
+re that exists, dummy?", "\n"; 
    while(readdir $currentDirectory) {
      chomp $_;
      push(@contentsOfDirectory, $_);
    }
  closedir $currentDirectory;

}

@contentsOfDirectory = grep (!/^\./, @contentsOfDirectory);
my @minus = array_minus( @contentsOfDirectory, @contentsOfDataBase );
my @minus2 = array_minus( @contentsOfDataBase, @contentsOfDirectory);

print "\n", "These files have PDFs and no database entries:", "\n", "\
+n", "\n";

foreach (@minus){
  print "\n", "$_ ", "\n";

}

print "\n", "These files have databse entries and no PDFs:", "\n";

foreach (@minus2){
  print "\n", "$_ ", "\n";

}
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