Here are the changes that I have made.

#    AGTS-CLI(Andrew's GTK Time System-Command Line version)
#    Copyright (C) 2008  Andrew Harris
#
#    This program is free software: you can redistribute it and/or mod
+ify
#    it under the terms of the GNU General Public License as published
+ by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.
#
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.
#
#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, email andrew2325@gmail.com!
#    Contributors:  Kelly Royal <netdaemon862@gmail.com>
#!/usr/bin/perl
use strict;
use warnings; 
my $time = localtime;
sub verify {
    my $username = shift;
    my %logins = shift;
    if (exists $logins{$username}) {
        login($username, %logins);
    }
    else {
        print "$username does not exist in our database.\n";
    }
}

sub login {
    my %logins = shift;
    my $username = shift;
    print "Enter your password: ";
    chomp(my $pass = <STDIN>);
    if ($pass <=> $logins{$username}) {
        greeting($username);
    }
    else {
        print "Incorrect password!\n";
    }
}

sub greeting {
    my $username = shift;
    print "Welcome $username.\n";
    print "Current time is $time\n\n\n";
}

sub admin {
    my %logins = shift;
    print "Administrative Tools\n";
    print "1. Add user\n";
    print "2. Remove user\n";
    print "Enter selection: ";
    chomp(my $selection = <STDIN>);
    if ($selection == "1") {
        print "Enter new user name: ";
        chomp(my $newname = <STDIN>);
        print "Enter password for $newname: ";
        chomp(my $newpass = <STDIN>);
        $logins{$newname} = $newpass;
        print "User added.\n";
    }
}
while (1) {
print "Welcome, Main Menu\n";
print "1. Log in\n";
print "2. Log out\n";
print "3. Administration\n";
print "Enter selection: ";
my $selection = <STDIN>;
my %logins = ("kroyal" => "5678", "aharris" => "1234");
if ($selection == "1") {
    print "Enter your user name to log in: ";
    chomp(my $username = <STDIN>);
    verify($username, %logins);
    open(MYLOGINFILE, ">>login.txt");
    print MYLOGINFILE "$username:$time\n";
    close(MYLOGINFILE);
}
elsif ($selection == "2") {
    print "Enter your user name to log out: ";
    chomp(my $username = <STDIN>);
    verify($username);
    open(MYLOGOUTFILE, ">>login.txt");
    print MYLOGOUTFILE "$username:$time\n";
    close(MYLOGOUTFILE);
}
elsif ($selection == "3") {
    admin(%logins);    
}
}
[download]

Now when I run it, only one of the default users work and you can't add users. I get the following errors when logging in:
Welcome, Main Menu
1. Log in
2. Log out
3. Administration
Enter selection: 1
Enter your user name to log in: aharris
Odd number of elements in hash assignment at ./maybe.pl line 23, <STDIN> line 2.
Odd number of elements in hash assignment at ./maybe.pl line 33, <STDIN> line 2.
Enter your password: 1234
Use of uninitialized value $logins{"aharris"} in numeric comparison (<=>) at ./maybe.pl line 37, <STDIN> line 3.
Welcome aharris.
Current time is Mon May 5 11:58:30 2008