my @Required = qw( ... );
my @Non_Zero = qw( ... );

unless ((grep { $row->{$_} eq '' } @Required) ||
        (grep { $row->{$_} == 0  } @Non_Zero))
{
    # Do stuff here with $row now that we have all the
    # Required and Non_Zero fields verified...
}
else
{
    &complain($row);
}