Have a look around for error messages in your logs etc. (and consider using the DBI 'RaiseError' etc.), but I suspect this might be to do with quoting in your SQL statements. Try using $dbh->quote() something like this...

my $query = "UPDATE staff 
            SET password=".$dbh->quote($FORM{'newpassword'}.
            " WHERE ".$dbh->quote($FORM{'name'}).
            " =". $dbh->quote($record{'login'});
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....or in a less clumsy way than this, if you like :)