This may be slightly cleaner:

my @where;
my @full_entries = grep { length } @entries;

for (0..$#fields) {
        push @where, $fields[$_], $full_entries[$_]
                if defined($fields[$_] && $full_entries[$_]);
}

my $sql = "SELECT " . join(", ", ('?') x @fields) . " FROM HELP WHERE 
+(" . join(" AND ", ("? LIKE ?") x @fields) . ")";

$dbh->prepare($sql);
$dbh->execute(@fields, @where);
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[ar0n]