Another implemenation based on Rolf's suggestion:

#!/usr/bin/perl
use strict;
use warnings;

while (my $line = get_CSVline())
{
    print "$line\n";
}    

sub get_CSVline
{
   my $buffer;
   
   while (!defined($buffer) or is_odd_quotes($buffer) )
   {
      my $temp =<DATA>;
      $buffer .= $temp;
   }

   chomp $buffer;
   $buffer =~ s/\n/\\n/g; #### make "\n" "visible" ###
   return $buffer;
}
            
sub is_even_quotes
{
   my $string = shift;
   return !( ($string=~tr/"//) % 2);
}

sub is_odd_quotes
{
   my $string = shift;
   return ( ($string=~tr/"//) % 2);
}

=PRINTS:
1,2,3.3,"\n",4,5
6,7,8,9
6,"\n",7,8
a,b,c,"something\nmore"
1,2,3
1,"x\n","y","z\n",3
"3.5 "" disks"
=cut

__DATA__
1,2,3.3,"
",4,5
6,7,8,9
6,"
",7,8
a,b,c,"something
more"
1,2,3
1,"x
","y","z
",3
"3.5 "" disks"
[download]

Update: Added one more test case.
Added the '"3.5 "" disks"' test case.