I have the same problem. I can't access to live chat on my laptop at all but on my mobile phone I can access but only when I'm not log in to my 3 account, if I log in to 3 account it show nothing for live chat. Maybe you should try without log in.
Hope it help.
I can't get access to live chat. They would't set it up in the three store and now the oneline setup wont work. How do I get access to live chat? This is all I get now "Sorry, no one's here to chat with you right now. Our operators are online from 7am to 11:45pm Monday to Sunday."