Hello,
the plugin jQuery Easy re-orders the libraries in the header to make sure it loads MooTools, jQuery and jquery no conflict code first. It does not do any other modification. The plugin is not responsible for any of the code that is loaded by the modules.
The line:cannot work on your site for instance, because the '$' is used by MooTools and here one of your modules loaded this line for jQuery (colorbox). So you have conflict.
It should be something like
Also, some script that was supposed to be added through the jQuery Easy plugin was not (ADD_SCRIPT_DECLARATION_HERE is present and has not been replaced by your code for some reason)

You also have duplicated script code, but that may just be that you have several instances of the same module.

At this point, there are too many problems, you need to treat them one at a time. Start with colorbox.

Sorry, I did not see: the code $j = new Object();... in the 'add script declaration' of the plugin is probably your main problem...

You cannot use
var $j = jQuery.noConflict();
You just cannot use '$' for jQuery. Once again, it conflicts with MooTools.
You do not need this line, just replace
$j(document).ready(function(){...}
with
jQuery(document).ready(function($){...}
and all jQuery calls inside { ... } can start with $.

Also, you do not need var dinamods = jQuery.noConflict();
Dinamod is not written using jQuery.