Well, it doesn't do all the magic for you, but quite a bit:

#!/usr/bin/perl
use warnings;
use strict;

my (@nodename, @filename, @pathname, @backupdate);
use Data::Dumper;

{
    # discard heading line
    my $tmp = <DATA>;
}
while (my $line = <DATA>){
    chomp $line;
    my ($nn, $fn, $pn, $bd) = unpack('A8xA9xA8xA15', $line);

    if ($nn =~ m/\S/){
        push @nodename, $nn;
        push @filename, $fn;
        push @pathname, $pn;
        push @backupdate, $bd;
    } else {
        $nodename[-1] .= $nn;
        $filename[-1] .= $fn;
        $pathname[-1] .= $pn;
        $backupdate[-1] .= $bd;
    }
}
print Dumper([\@nodename, \@filename, \@pathname, \@backupdate]);


#1234567890123456789012345678901234567890123
__DATA__
NodeName FileName  PathName  BackupDate
BD3101   bananaswi \breakfa       2007-03-06
         ithapple  st\fruit  14:02:31.000000
         s.gif     s\tree\                  
TP4223   chocolate \sweet\d       2006-02-28
         caramelfu esserts\  21:16:41.000000
         dge.gif   hersheys\                
EO2123   tofuwith  \organic\      2007-07-16
         peas.gif  vegetable 13:55:06.000000
                   s\legumes\
[download]

Actually the data would better be stored in a two dimensional array.

Note that all lines that don't have the Backup Date field need to be padded with whitespaces at the end of the line to be long enough, if that's not the case you'd have to pad them manually before using unpack.