What fetchrow_array returns in scalar context is undocumented.
$data1 = $sth->fetchrow_array();
is wrong. If you want to the first field, use
($data1) = $sth->fetchrow_array();
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Is the contents of $dberror text of HTML? You put both into it. At wor
+st, this could be an opening for a cross-site scripting attack.
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All over, you are instructing Perl to ignore prototypes. Why do you us
+e & on your subroutine calls?
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I note a distinct lack of my. Use use strict;!
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Something tells me you don't use warnings either. ("if ($data1 ne $dig
+est1)" would warn if fetchrow_array returned zero rows.) Use use warn
+ings;!
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Why is six in quotes in "if (scalar @row1 == "6")"? You want to compar
+e with the number 6, not the string "6" (which would be converted to 
+a number by ==). The scalar is useless too. == creates a scalar conte
+xt, so scalar is redundant.
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if (@row1 == 6) {
     other code here ...
};
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for my $row ( 1 .. $#rows ) {
   if (@{ $rows[$row] } == "6") {
      my @entry = (@required , @row);
      ...
   }
}
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I do not understand what you mean by stating I put both into it?

@entry1 contains text and not HTML, right? At the very least, it needs to visit HTML::Entities.

I was under the impression that this was proper usage

It disables prototypes and allows subroutines to be called without parens before they are declared. It was possibly the way to do things in Perl4, but this isn't Perl4.

the primary reason in using "my()" is so that the variables are completely hidden from the outside?

Yes. It limits the scope of the variables. This prevents accidental clobbering of the variables by distant code and it fosters modularity of code. In conjunction with use strict;, typos in variable names are usually caught at compile-time. use strict; helps identify a couple of other type of dangerous code.

   my @entry = (@required , @{$rows[$row]});
   my $digest = sha1_hex(@entry);
   my $sth = $dbh->prepare($query);
   $sth->execute($digest);
   my ($data) = $sth->fetchrow_array();
   ...
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I actually want it to return with zero rows

Yes, but you don't want it to warn "Use of uninitialized value in string eq" when it does. defined would be one way of avoiding the warning.

So if I read what you stated, I could accomplish the same thing by doing this

Yes. @row1 == 6 checks if @row has 6 elements. An array in scalar context (as imposed by scalar but also by ==) evaluates to the number of elements in the array.

In trying to understand how this statement works

All variables other than @row1 can lose the "1" without problem. The rows are a little bit trickier since we want to switch to using a loop. Unfortunately, you haven't shown us everywhere @rowX is used — in particular, you haven't shown us where they're created — so our help there is limited.

Basically, I suggested that you create an array @rows whose elements are references to arrays (formerly @row1, @row2, etc). This is commonly called an "array of arrays". Basically, Perl's version of a two-dimensional array. There's perllol on the subject, for starters.

Note: I've updated my post to fix a bug in that code.

Thank you again for your response. I was hoping I could provide this snippet and take what I learn from it and clean up my entire script. However, it appears as if I may need to show you my entire script to ensure I don't shoot myself in the foot later. I appreciate the time you've already spent on this with me but would you be willing, if I show you my entire script, to provide me with some guidance/suggestions to get my script cleaned up?