If you were running with "use warnings" then Perl would have told you what the problem is. Filehandles aren't first-class variables in Perl so you can't just return a filehandle from a function and assign it to a variable like that. You're actually using the same filehandle (FILE) for both files - which is why you can't use it after you've closed the first filehandle.

You can get round this by using lexical filehandles.

sub openFile {
  my ($file, $accessMode) = @_;
  my $err;

  $accessMode = $MODE_READ unless defined $accessMode;

  if (exists($ACCESS_MODES{$accessMode})) {
    if (open(my $fh, "$ACCESS_MODES{$accessMode}$file")) {
      return $fh;
    } else {
      $err = $!;
      if (defined($returnOnError)) {
        return;
      }
      &throwGenError("Can't open $file: $err");   # throw exception
    }
  } else {
    &throwGenError("In openFile: Wrong access mode &accessMode");
  }
  return;
}
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Some of your logic is a bit scary, so I haven't changed too much. You might need to check it carefully.