Welcome to the Community!
If your brother's account is still active, you can opt to continue the same account, although it will now be a question of how the bill will be paid since most likely, the card details are of your brother's. The other option is for a request of Change of Ownership but your brother needs to be the one to request of it. In the event that you wish to set up a new account, depending on the service technology, your brother may need to cancel his account first.
As for the NBN box being thrown out, that definitely needs to be addressed. In order to have a better idea of the best approach on how we can provide you a service, would you be able to PM us your brother's TPG account username or customer ID along with the service address?
For your reference: How do I private message (PM) in the community