Use a hidden field:

#!/usr/bin/perl -w

# fatalsToBrowser as early as possible.
use CGI::Carp qw(fatalsToBrowser); 

use strict;  # You really should!

# Load other modules.
use CGI qw(:standard);

my $oldtable = param('oldtable');

if (not defined $oldtable) {
   # XXX CGI script shouldn't die;
   #     They should return an HTTP error
   #     with an HTML error message to the
   #     client.

   die("This document must be opened with the oldtable parameter\n");
}


print start_html(
         -title   => foo,
         -BGCOLOR => bar,
         -style   => { 'src' => foo, 'title' => bar }),
      start_form,
      radio_group(
         -name   => 'sortby',
         -values => [ 'Sort by foo', 'Sort by bar' ]),
      p,
      hidden(-name => 'oldtable' -value => '0', -override => 1),
      submit(-name => 'search',  -value => 'Search'),
      end_form;


if ($oldtable) {
   foo;
} else {
   bar;
}
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