How to jump to another know page on a button click?
If the whole implementation (including the URL computing) is done on the client side with javascript then the easiest solution would be to simply use code like the following:

$('#go_button_id').click(function() {
  location.href = 'url_to_the_computed_page';
});


On the server side you could use Drupal's block hooks and form API to create a block with a simple form and then use $form_state['redirect'] = 'url_to_the_computed_page'; in the form submission handler for the redirect.