An inner $p->get_tag() loop is needed.

use strict;
use warnings;

use HTML::TokeParser;
my $p = HTML::TokeParser->new( *DATA );

while (my $token = $p->get_tag('select')) {
  my $name = $token->[1]{name} ;
  my $option_text = '';
  while (my $token2 = $p->get_tag('option', '/select')) {
    last if $token2->[0] eq '/select';
    if ( $token2->[0] eq 'option' and $token2->[1]{selected} ) {
      $option_text = $p->get_trimmed_text();
      last;
    }
  }
  print "\$name = '$name', \$option_text = '$option_text'\n";
}
__DATA__
<TD style="HEIGHT: 29px">
    <select name="cmbPurpose" id="cmbPurpose" tabindex="3">
    <option value="CD">Cell Development</option>
    <option value="MS">Miscellaneous R&amp;D</option>
    <option value="NP">New Package</option>
    <option value="NR">Non R&amp;D</option>
    <option value="PC">New process</option>
    <option selected="selected" value="PD">New product</option>
    <option value="SP">Sustaining Product</option>
    <option value="SW">Software and Platform</option>
    <option value="TD">Technology Development</option>
</select></TD>
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