Unfortunately you won't be able to use LiveChat even if you had your phone number - at&t's LiveChat option is only for post paid accounts. 
I would either visit your local at&t store and they should be able to assist you with activating a prepaid account, or you can contact customer service by calling 1-800-331-0500 and selecting "more options" at the first automated prompt, and then state "customer service" at the following menu prompts. Eventually you will be connected to a live representative.
You don't really say, but I presume you do have a SIM card to go with your new prepaid cell phone? As you do need the SIM card in addition to the refill card - so if you don't have a SIM, I would just visit your local at&t store - you'll be able to walk out with a working phone. 