The following code will give you the desired output:

#!/usr/bin/perl -w
use strict;

my %users;
my $username;

while (<DATA>) {
    next if (/^\s*$/);
    chomp;
    if (/^Username\:\s+([A-Z]+)\s+Owner\:\s+(.*)$/) {
        $username = $1;
        $users{$username}{realname} = $2;
    }
    elsif (s/^(Last Login\:\s*)//) {
        ($users{$username}{i}, $users{$username}{ni}) = split /,/, $_;
    }
    else {
        die "line invalid - $_, $!\n";
    }
}

foreach my $user (keys %users) {
    print
        "$user,$users{$user}{realname},$users{$user}{i},$users{$user}{
+ni}\n";
}

__DATA__
Username: JANDERSON                            Owner:  JOE ANDERSON
Last Login: 14-JAN-2002 08:14 (interactive),  4-MAR-2002 17:09 (non-in
+teractive)
Username: PBARRETT                           Owner:  PAUL BARRETT
Last Login: 18-JAN-2006 08:14 (interactive),  24-MAR-2005 17:09 (non-i
+nteractive)
[download]

Comments:

• Your main problem is that you weren't correctly assigning to the hash. Instead of $login_times{ni} you need something like $login_times{$user}{ni]
• There is no need to quote your hash elements if they don't contain whitespace (it just makes the code more confusing)
• I re-named your hash as %users, so it makes more sense
• Your username pattern match was capturing all the whitespace following the username. If you can assume that all usernames will be uppercase letters only, then you could re-write that as /^Username\:\s+([A-Z]+)\s+Owner\:\s+(.*)$/

I should also note that the above code is quite fragile, insofar as it assigns the $username when it reads the first line, and then assumes that the username is the same when it gets to the second line. There are probably much better ways to go about this, which no doubt some other monks will point out :)

Cheers,
Darren :)