I can't see how they can stop you connecting to wi-fi if you have a router or can go to McDonalds or similar to join their network. All the service provider can prevent is you making calls and sending text messages. The phone itself if a computer and you can still go online through an existing route which includes a Hotspot your could set up on your new phone.
All that said, my best suggestion is for you to backup the device within itself, on to a micro SdCard.
Buy one if you don't have one because the system will work deactivated or not and ou can take the card out afterwards and put it in the new phone.