Without knowing more about your code it's difficult to know what's going on there. There's probably something wrong in my JS (sorry). Have you tried adding a breakpoint to the first if test in the display_popup() function? If you do so and walk through you should be able to determine whether dialogue.show() is being reached.
It shouldn't be necessary to have the dialogue created on page load to get the URL parameters, but equally, you can pass parameters into the yui_module call with:
$PAGE->requires->yui_module('moodle-local_pluginname-mypluginname', 'M.local_pluginname-yuimodulename', array(array( 'param1' => 'value1', 'param2' => 'value2', ));
These values will then be passed into your function at startup.
Rendering and showing a new dialogue is fairly expensive (computationally) and is best avoided until required.
Is your code online somewhere and I may be able to help further?