there has existed for somehing like 35 years an analogue modem for 27MHZ, 142MHZ licenced and unlicensed. It's just a little PCB you solder to your mike / speaker points. There are multiple private 24/7 uplinks around the world. so you can mail and surf as you would normally, but slow. Around 2K baud, So try to sync your block chain on that.
As a post apocalyptic internet it's fine.
This sounds really interesting. Any chance on a link to more info?
Here you go, it's called a TNC:
http://www.coolcircuit.com/gadgets/category/ham-radio/ There are 100+ pages about them.
Apparently there are also micro processor versions now...
BTW there are also free HAM satellite repeters for voice and data:
http://www.amsat.org/amsat-new/index.php