Thanks Rolf!

I believe I was able to make your idea work. I've posted a solution below, feel free to critique if you have the notion.

my $wait_for_odd_quotes = 0;
my $line_accumulator = '';
while(<$CSVFILE>) {
    chomp(my $this_line = $_);

    my @matches = $this_line =~ /(\")/g;
    my $count = @matches;

    if($wait_for_odd_quotes == 0){
        if($count % 2 == 1){
            $line_accumulator = $this_line; #Reset Accumulator
            $wait_for_odd_quotes = 1; #Prime next loop to look for end
+ of quotes
        }
        else {
            print $OUTFILE $this_line . "\n"; #We are not looking for 
+and end quote and this line doesn't have an odd number of quotes so w
+e'll write it to file
        }
    }
    else {
        if($count % 2 == 1){
            $line_accumulator .= $this_line; #matched our open quotes,
+ taking this last bit
            $wait_for_odd_quotes = 0; #reset so next loop knows we're 
+not looking to close
            print $OUTFILE $line_accumulator . "\n"; 
        }
        else {
            $line_accumulator .= ' ' . $this_line;
        }
    }
}
print $OUTFILE $line_accumulator . "\n"; #catch final line if it had e
+mbedded newlines
[download]

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.

Just a minor nitpick, your test cases doesn't cover an escaped double quote.

Adding a line like ,"3.5 "" disks", might help. :)

edit

And you wouldn't need to check defined $buffer if you used a do-while loop.

Cheers Rolf
_{(addicted to the Perl Programming Language and ☆☆☆☆ :)
Je suis Charlie!}

Regarding LanX's suggestion: Remove Tabs and Newlines Inside Fields of Text Tab Delimited Files from Excel.

Untested for comma delimiters, but presumably you would just have to change all the split and join lines to use commas instead of tabs.

Also, from another post: Do I have to trick Split? Using "-1" for the third split parameter fixed some warnings trailing empty data columns caused during the subsequent join.

my @data = resolve_comma_delimited_file_line($CSVFILE, $this_line);

# This subroutine accepts a filehandle and a line read from that fileh
+andle as arguments given in that order.
# If necessary it will modify the line that was passed to it (as if pa
+ssed by reference) to resolve it, and return an array of the split da
+ta.
sub resolve_comma_delimited_file_line
{
    my $fh = $_[0];
    chomp($_[1]); # $_[1] being the read line passed in to this subrou
+tine that is to be modified if necessary (as if passed by reference)
    my @data = split /,/, $_[1], -1;
    
    my $last_index = $#data;
    for (my $field_index=0; $field_index<$last_index; $field_index++)
    {
        if (($data[$field_index] =~ tr/"//) % 2 == 1)
        {
            splice @data, $field_index, 2, "$data[$field_index] $data[
+$field_index+1]";
            $_[1] = join ",", @data;
            $last_index--;
            $field_index--;
        }
    }
    if (($data[$last_index] =~ tr/"//) % 2 == 1)
    {
        $_[1] .= " " . <$fh>;
        @data = &resolve_comma_delimited_file_line;
    }
    
    return @data;
}
[download]

UPDATE: Deleted comments related to tabs since they wouldn't be relevant for the comma case.

That being said, Text::CSV is still probably a better option because it saves you from having to "reinvent the wheel" so to speak, and probably is a lot more robust solution for the types of hiccups you may encounter in your file data.

Just another Perl hooker - will code for food