#!/usr/bin/perl
use strict;
use warnings;
use Text::xSV;

my $csv = Text::xSV->new( fh => *DATA );
$csv->bind_header;
while ( $csv->get_row() ) {
    my $row = $csv->extract_hash();
    print $row->{Domain}, "\n";
}
__DATA__
"Column 1","Company Name","Column 2","Domain","Status","Start Date","E
+xpiration
Date","Renew Date"
"1495107228781574","SomeCompany, Inc.","8335788590132972","kerpow.org"
+,"Active",
"Jan 27 2000 9:02PM","May 1 2004 12:34PM","May 28 2005 2:02AM"
"1495107228781574","SomeCompany, Inc.","1802975834647670","squish.com"
+,"Active",
"Jul 15 2004 1:49PM","May 2 2004 11:05PM","May 19 2005 11:05PM"
[download]

Try this on for size. It reads your file using the standard Text::CSV_XS module and prints just the domain field.

use strict;
use warnings;
use constant {
    FIELD_Unknown_1 => 0,
    FIELD_CompanyName => 1,
    FIELD_Unknown_2 => 2,
    FIELD_Domain => 3,
    FIELD_Status => 4,
    FIELD_Unknown_3 => 5,
    FIELD_Unknown_4 => 6,
    FIELD_Unknown_5 => 7,
};
    
my $parser = Text::CSV_XS->new();

while ( my $line = <> ) {
    $parser->parse( $line );
    my @columns = $parser->fields;

    my @new_columns = @columns[
        FIELD_Domain,
    ];
    $parser->combine( @new_columns );
    print $parser->string;
}
[download]

#!/usr/bin/perl
use strict;
use warnings;
 
while (<DATA>) {
   my $domain = (split /","/,$_,5)[3];
   print $domain,"\n";
}
 
__DATA__
"1495107228781574","SomeCompany, Inc.","8335788590132972","kerpow.org"
+,"Active","Jan 27 2000 9:02PM","May 1 2004 12:34PM","May 28 2005 2:02
+AM"
"1495107228781574","SomeCompany, Inc.","1802975834647670","squish.com"
+,"Active","Jul 15 2004 1:49PM","May 2 2004 11:05PM","May 19 2005 11:0
+5PM"
"1495107228781574","SomeCompany, Inc.","4430459098697337","wanka.com",
+"Active","Nov 9 2004 9:29AM","May 3 2004 2:14PM","May 16 2005 2:14PM"
"1495107228781574","SomeCompany, Inc.","2113292909703608","blah.com","
+Active","Jan 16 2003 10:48AM","May 4 2004 12:34PM","May 16 2005 5:48A
+M"
[download]

In my case, I'm getting static stocks data from Yahoo Finance and I expect it to be in a certain order, so I just split it, and only take what I'm after. If your data is going to change, then this isn't going to do it for you. HTH

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

my @results;
my $relevant;

while (<DATA>){
   (undef, undef, undef, $relevant) = split ('","',$_);
   push(@results, $relevant);
}

print join("\n", @results);

__DATA__
"1495107228781574","SomeCompany, Inc.","8335788590132972","kerpow.org"
+,"Active","Jan 27 2000 9:02PM","May 1 2004 12:34PM","May 28 2005 2:02
+AM"
"1495107228781574","SomeCompany, Inc.","1802975834647670","squish.com"
+,"Active","Jul 15 2004 1:49PM","May 2 2004 11:05PM","May 19 2005 11:0
+5PM"
"1495107228781574","SomeCompany, Inc.","4430459098697337","wanka.com",
+"Active","Nov 9 2004 9:29AM","May 3 2004 2:14PM","May 16 2005 2:14PM"
"1495107228781574","SomeCompany, Inc.","2113292909703608","blah.com","
+Active","Jan 16 2003 10:48AM","May 4 2004 12:34PM","May 16 2005 5:48A
+M"
[download]

Output:

kerpow.org
squish.com
wanka.com
blah.com

Popcorn Dave,

Okay, this absolutely sits side by side with the sunrise, that I so was lucky
to be able to witness this morning...

I'm going to walk through the other responses as well so I can see the different
ways to approach and visualize this data! THANK YOU! :)


Oh yeah, I also wanted to give you a blurb of, 'this is was what I did to make
this work on my end.'

I took this line of code:
while (<DATA>){

and changed it to this:
while (<>){

so I could make the module read from STDIN and direct it to the new file:
./wicked.pl thefile.txt > thedataIneed.txt

and like I said above...WOW!! What a beautiful sunrise!

Simone~

split ('","',$_);

While this split works on the data set presented, it is definitely not a good general solution for CSV parsing. There are at least two kinds of valid CSV that will break it. In the first place, many CSV generators omit quotation marks around fields that don't contain embedded special characters so this is a valid three-field CSV record in braces: {foo,"a,b",7} in which the quote-comma-quote split would fail because there are not quotes around some of the field-separating commas. Also, if there are embedded quote marks in the data, those are usually escaped by doubling the quote marks so this is also a valid three-field CSV record: {7,"a"",""b",8}, in which the split would fail because it would find a non-field-separating quote-comma-quote pattern.

No, you're right, I see that now, and that's a very good point. I was just trying to show something that I had used, with the caveat that it may or may not work for the OP's data. In my particular case, the data is just CSV so just a split on ',' with the undefs works.
Useless trivia: In the 2004 Las Vegas phone book there are approximately 28 pages of ads for massage, but almost 200 for lawyers.