$SQL = "SELECT COUNT(*) FROM Members WHERE Nickname = ?";
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Your question should be answered by one of the nodes above, but just a note for the future: when debugging DBI, use the DBI->trace() method to turn on extra debugging information printed to STDERR. Usually a trace level of 2 is sufficient, which should show you (among other things) the statement after placeholders are filled in.

my @row = $Statement->fetchrow_array;
if ($row[0] > 0)
{
    LogError("NICK_TAKEN");
    return("-1");
}
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  $rv = $sth->rows;
    Returns the number of rows affected by the last row affecting comm
+and, or -1 if the number of rows is not known or not available.

    Generally, you can only rely on a row count after a non-SELECT exe
+cute (for some specific operations like UPDATE and DELETE), or after 
+fetching all the rows of a SELECT statement.

    For SELECT statements, it is generally not possible to know how ma
+ny rows will be returned except by fetching them all. Some drivers wi
+ll return the number of rows the application has fetched so far, but 
+others may return -1 until all rows have been fetched. So use of the 
+rows method or $DBI::rows with SELECT statements is not recommended.

    One alternative method to get a row count for a SELECT is to execu
+te a "SELECT COUNT(*) FROM ..." SQL statement with the same "..." as 
+your query and then fetch the row count from that.
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• Check the result of your prepare.
• Check the result of your execute.
• Don't quote placeholders.
• Why check the number of rows returned (which might not even available until all rows have been fetched)if you are doing a count (*)?
• Why quote the -1 you are returning?

Two things:

• Drop the single quotes around the ? mark to make the syntax right
• As you use count in your SQL statement, you will always get one row back, thus checking the size of result set makes no sense, simply use the count you get.

If you just want to see whether a value appears in a column of a table, performing a count(*) is a fearfully expensive way of going about that. At the worst, you will perform a full table scan.

The query would be better formulated as select 1 from members where nickname='...'

If this is just a once-off, the simplest approach would be to use the do method, with something (error-checking notwithstanding) like:

sub nick_exists {
  return $db->do( "select 1 from members where nickname="   
    . $db->quote($_[0])
  );
}
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If, on the other hand, you know you'll be pounding on this routine in an inner loop, it might then be worthwhile recasting it as a prepared statement:

BEGIN {
my $ss = $db->prepare( 'select 1 from members where nickname=?' ) or d
+ie;

sub nick_exists {
    $ss->execute($_[0]);
    my $res = $ss->fetchrow_arrayref;
    $ss->finish;
    $res and defined $res->[0] ? 1 : 0;
}
}
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The beauty of this approach is that you don't have to change your code. The access to the database is abstracted away in the nick_exists routine.

And as if that wasn't enough, you could further add

use Memoize;
memoize('nick_exists');
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... although you want to be careful with that. The program will continue to assume that a nick that has just been taken is still available. That would be a bug. But, used with care, this can provide a healthy speed boost.