Your question makes no sense to me, maybe you can simplify it by posting running code that reproduces your problem (as per How do I post a question effectively?), something like

#!/usr/bin/perl --
use strict;
use warnings;
use CGI::Pretty;
my @fudge = 1..3;
my $q = CGI::Pretty->new ( { class => \@fudge } );
print "{$_}\n" for $q->param('class');
print $q->checkbox_group(-name=>'class'), "\n"
__END__
{1}
{2}
{3}
<label>
         <input type="checkbox" name="class" value="1" checked="checke
+d" />1
</label>
<label>
         <input type="checkbox" name="class" value="2" checked="checke
+d" />2
</label>
<label>
         <input type="checkbox" name="class" value="3" checked="checke
+d" />3
</label>
[download]

Sorry, I was trying to avoid copying and pasting so much since I have everything on a UNIX server at school. Here is the checkbox HTML. It is a separate file from the cgi file.

<hr>
<b>Pearl Parks and Recreation Class Listings</b>
<p>
Please use the checkbox(es) to indicate which class/classes you would 
+like to register for. <p>
<table border="1" cellpadding="4">
<tr>
  <th></th>
  <th>Title</th>
  <th>Location</th>
  <th>Time</th>
  <th>Start</th>
  <th>Cost</th>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Pilates"></td> 
  <td>Pilates (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>9am Sat</td>
  <td>9/10/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Zumba"></td> 
  <td>Zumba (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>10am Sat</td>
  <td>9/10/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Tai Chi I"></td> 
  <td>Tai Chi I (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>12pm Sat</td>
  <td>9/10/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Tai Chi II"></td> 
  <td>Tai Chi II (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>1:30pm Sat</td>
  <td>9/10/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Hatha Yoga"></td> 
  <td>Hatha Yoga (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>11:00am Sun</td>
  <td>9/11/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Yoga for Power"></td>
+ 
  <td>Yoga for Power (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>9:30am Sun</td>
  <td>9/11/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value=5K Team-Beginner"></td
+> 
  <td>5K Team-Beginner (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>8:00am Tue</td>
  <td>9/13/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Cycle Spin Youth & Fa
+mily"></td> 
  <td>Cycle Spin Youth & Family (11-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>5pm Tue/Thu</td>
  <td>9/13/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Low Impact Aerobics">
+</td> 
  <td>Low Impact Aerobics (13-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>5pm Wed</td>
  <td>9/14/2011</td>
  <td>$100</td>
</tr>
<tr>
  <td><input type="checkbox" name="class" value="Weight Training for W
+omen"></td> 
  <td>Weight Training for Women (16-Adult)</td>
  <td>Pearlview RECenter</td>
  <td>11am Wed</td>
  <td>9/21/2011</td>
  <td>$100</td>
</tr>
</table>
<br>

<input type="submit" value="Register!">
<input type="reset" value="Clear Form">
</form>
</body>
</html>
[download]

Here is the full cgi program that I've written so far. Note that this is still a work in progress.

#!/opt/csw/bin/perl
use CGI qw/:standard/; 

my $name = param('name');
my $address = param('address');
my $city = param('city');
my $state = param('state');
my $zip = param('zip');
my $phone = param('phone');
my $fax = param('fax');
my $email = param('email');
my $email2 = param('email2');
my $gender = param('gender');
my $invoice = param('invoice');

print header(),
start_html('Registration Confirmation'), 
hr(),
h2("Pearl County Parks and Recreation"), 
h4("Class Registration Confirmation"),
hr(),
p("Thank you for registering with Pearl County Parks and Recreation.")
+,
p("Please find your class registration confirmation below."),
hr(),
p("Name:",$name),
p("Address:",$address),
p("City:",$city),
p("State:",$state),
p("ZIP:",$zip),
p("Phone:",$phone),
p("FAX:",$fax),
p("Email:",$email), br(),

hr(),
hr(),

p("You are registered for the following class(es)."),  
p("As requested, your invoice will be sent to you by $invoice."), 
br(),

my @classes = param('class');
foreach my $class (@classes){
  print "$class <br>\n";
}

end_html();
[download]

Upgrade CGI.pm

The code you posted should never produce the output you described -- like this says, try upgrading CGI

While I doubt it's your problem, you might want to fix up the following line of HTML:

<td><input type="checkbox" name="class" value=5K Team-Beginner"></td>

I think you're missing a " after value=