The button on the main page and the button in the sliding panel, both whos mission it is to open the panel, has the same ID, #open
.
ID's must be unique, and jQuery will only work for the first ID with that name, and that's why it's not working with the link on the page.
You can give the link on the main page another ID, and just trigger the click event, like so:
$("#link_on_main_page_id").on('click', function(){
$('#open').click();
});