First of all, the reason your code doesn't work is that you are using single quotes in insertOnlineUsers().
Before diving headlong into objects, you should understand what the features such as inheritance should be used for. Inheritance is used to specialise a class.
In your case UsersOnlineSystem does not specialise class Users or class Base. A good litmus test to take is asking yourself 'is class B a type of class A' when considering inheritance. If the answer is no, the best approach is to use composition instead.
class core {
var $PAGE;
function core() {
$this->PAGE='test';
}
}
class User
{
var $USERNAME;
function loginCheck()
{
...sql query... $this->USERNAME=$row['USERNAME'];
}
}
class UsersOnlineSystem
{
function insertOnlineUsers( $users, $core )
{
...sql query... INSERT blah blah VALUES ($users->USERNAME,$core->PAGE);
}
}
$core = new Core;
$users = new Users;
$users->loginCheck();
$online = new UsersOnlineSystem;
$online->insertOnlineUsers( $users, $core );
On a sidenote, a class without properties has no business being a class.