It depends what you mean by "new internet," and how much control the government eventually takes over the actual hardware routing the current Internet. Even If the government owns every ISP, you could take part in encrypted communication, and I don't think there's any way for them to stop that. At the absolute worst, you could go back to basics, and just use the plain old telephone system to dial into known servers.
".. government owns every ISP, you could take part in encrypted communication, and I don't think there's any way for them to stop that.."
Sure they could: just disallow any "unknown" encrypted communication. For example requiring the en/decryption to happen at the ISP or only allowing traffic they can decrypt and check.
(I'm not saying this is likely, but it could be implemented and most folks wouldn't care)
> Sure they could: just disallow any "unknown" encrypted communication.
Even then, it's impossible to prevent arbitrary communication. You can always hide your message inside of allowed messages (steganography), or an even more basic albeit inefficient technique: just use the timing between allowed messages to encode your hidden message.
