Does it have to be HTML::TreeBuilder? If not this might be useful.

#!/usr/bin/perl

use strict;
use warnings;
use Data::Dumper;
use HTML::TokeParser::Simple;

my $html = <<'EOHTML';
<table cellspacing="0" cellpadding="2" border="0" width="100%">
    <tr>
      <td width="20%" align="right" valign="top" bgcolor="#CCCCCC">
      <font face="arial, helvetica" size="2"><b>02:44 AM
      EDT</b></font><br>
      <font face="arial, helvetica" size="1">0:42
      (est.)</font><br></td>

      <td valign="top"><font face="arial, helvetica" size=
      "1">Speech</font><br>
      <font face="arial, helvetica" size="2"><a href=
      "/cspan/cspan.csp?command=dprogram&amp;record=142524675">U.S.-Ja
+pan
      Relations</a><br>
      Asia Society, Washington Center<br></font> <font face=
      "arial, helvetica" size="2" color="#CC0000">Ryozo Kato</font>
      <font face="arial, helvetica" size="1">, Japan</font></td>
    </tr>
  </table>
EOHTML


my $tp = HTML::TokeParser::Simple->new(\$html)
  or die "Couldn't parse string: $!";

my $start;
my @scraped;
while (my $t = $tp->get_token) {
  $start++, next if $t->is_start_tag('table');
  next unless $start;
  my $text = $tp->get_trimmed_text('br');
  push @scraped, $text;
}

my @keys = qw(time length type title org1 org2);

my %h_cpan = map {$keys[$_] => $scraped[$_]} (0..$#keys);

#for (0..$#keys){
#  $h_cpan{$keys[$_]} = $scraped[$_];
#}

print Dumper \%h_cpan;
[download]

Output:

---------- Capture Output ----------
> "C:\Perl\bin\perl.exe" _new.pl
$VAR1 = {
          'org2' => 'Ryozo Kato , Japan',
          'length' => '0:42 (est.)',
          'time' => '02:44 AM EDT',
          'org1' => 'Asia Society, Washington Center',
          'title' => 'U.S.-Japan Relations',
          'type' => 'Speech'
        };
> Terminated with exit code 0.
[download]

Couple of points.
The org key is in two parts. Also there is probably a more elegant way of loading the array into the hash.

Hope that helps.

Update: Changed the for loop to map.