OK, Had to make some changes, but I got what I wanted. I am showing just the while loop that has been driving me nuts. Here are the changes:

while(<$IN>){
    chomp;
    if (m/$start/) {
      $name = $1;
      next;
    } elsif (m/^record size:\s+(\d+)/) {
       $Hash{$name}{'record_size'} = $1;
       next;
    } elsif (m/^last record:\s+(\d+)/){
       $Hash{$name}{'last_record'} = $1;
       next;
    } elsif (m/^data byte count:\s+(\d+)/) {
       $Hash{$name}{'data_byte_count'} = $1;
       next;
    } elsif (m/^\s+index name:\s+(\w.*)/) {
       push(@{ $Hash{$name}{'indexes'} }, $1);
       next;
    }else{
       next;
    }
  }
    close $IN;
    
    foreach my $key (keys %Hash) {
        print $OUT "File: $key<BR>\n";
        print $OUT "\tRecord Size: $Hash{$key}{'record_size'}<BR>\n" i
+f defined $Hash{$key}{'record_size'};
        print $OUT "\tLast Record: $Hash{$key}{'last_record'}<BR>\n" i
+f defined $Hash{$key}{'last_record'};
        print $OUT "\tData Byte Count: $Hash{$key}{'data_byte_count'}<
+BR>\n" if defined $Hash{$key}{'data_byte_count'};
        if (defined $Hash{$key}{'indexes'}){
          my $str = join ', ', @{ $Hash{$key}{'indexes'} } ;
          print $OUT "Index Names: $str<BR><BR>\n";
        }else{ print $OUT "<BR><BR>\n"; }
    }
}
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I ran the hash through Data::Dumper and was seeing all of the data, but was having an issue printing. I then noticed that some fields were missing in the data, so I went back and verified that they didn't exist in the actual files. Once I did that, I put in the defined checks and everything worked.