Well, the short of it is that your code is incorrect.
jQuery(document).ready(brk.start($));
The $ here doesn’t refer to anything. You should change this to:
jQuery(document).ready(function($) { brk.start($) } );
With noConflict mode enabled, the $ value is not defined. If you want it to be defined, then you have to define it yourself.
This code:
jQuery(document).ready(function($) {
...
});
Does a couple things.
First, it hooks a function to the document.ready event. Secondly, it defines a function to call. Third, it sets the $ value to be jQuery for the code inside that function.
Your code was not defining a function nor setting the $ value. You were trying to call brk.start with a parameter of $ and then attach whatever the return value of it was to the document.ready.
The brk.start(whatever) is a function call, not a function definition itself. You need to define a function to attach it to a document.ready event.
Alternatively, this might work. I have not tested it.
jQuery(document).ready(brk.start);
The brk.start, without the parentheses, is a function and so it can be referred to in this manner. Maybe.
Although honestly, if you don’t want to attach the function call to document.ready and just want to call it in real time, then this would do the job:
brk.start(jQuery);