Components in 1.3 don't use the constructor for settings
The first significant problem you have is: the way components receive settings changed between major versions.
//Component(Collection) Class
$component->initialize($controller, $settings);
//ComponentCollection class
new $componentClass(ComponentCollectionObject, $settings);
Therefore the way to make the component work the same way in 1.3 - is to define the initialize method.
Helpers have a different constructor
A similar change was made to helpers:
//View class
new $helperCn($options);
//HelperCollection class
new $helperClass(ViewObject, $settings);
In this case it should be more obvious - any overridden method should have the same method signature as the parent class. Therefore: change the helper to have the same expected arguments in the constructor
Warning: extends Component
In 1.3, components do not extend Component, they extend Object. Component is the class which acts as a collection in 1.3, extending it will cause unexpected and undesired behavior (i.e. it'll likely cause unexpected "random" warnings and fatal errors). As such you should change the component class to be analogous to all other components, extending Object (or quite simply - not extending component).
If this class is something you use and maintain in various projects, it'd be a good idea to extract the main functionality into a standalone class, and implement only a thin wrapper class (component/behavior) to interface with it. In this way any changes made to the main functionality can be leveraged irrespective of the version of cake - or any other framework - used.