There are projects to build a new, decentralized internet. I heard from another project, that uses regular wifi routers to build a decentralized  p2p network (mesh network). There is still the possiblility to use your analogue telephone to connect with a dial-up connection.

Some links:

http://www.computerworld.com/article/2512713/internet/without-internet--egyptians-find-new-ways-to-get-online.html
https://nakedsecurity.sophos.com/2012/02/24/activists-creating-decentralized-mesh-network-that-cant-be-blocked-filtered-or-silenced/
https://www.deepdotweb.com/2014/11/04/decentralized-resistant-alternative-internet/
https://www.reddit.com/r/darknetplan/