There used to be free dial-up providers, usually the system doubled as a BBS or shared Unix system of some sort.
Obviously these smaller ones had a limited amount of concurrent connections, sometimes only 1 at a time.. Typically that required a level of trust that the users wouldn't horde it 24/7.
Today, it's not so easy.. bandwidth costs money, and people demand faster connectivity..
Now, "Open Internet" could be a private network.. separated from the Internet, meaning a separate root server infrastructure and re purposing IP ranges.
http://en.wikipedia.org/wiki/Alternative_DNS_root
You could setup a such a thing in your area, assuming you have interested friends willing to join the cause.. could use ad-hoc wireless or something. (
Or if you're a hammy, packet radio?).