Around the mid-80s a friend of mine set up a public-access Unix system. You could dial in and get shell access, and from there newsgroups, email, etc. It technically wasn't a "live" internet connection, his system dialed in to Yale each night and downloaded newsgroups and stuff via UUCP, so there was at least a day's delay between writing messages and getting a response. I don't remember exactly when it was but I was around for the Morris worm so it was some time before that.
M-Discs are not like standard Blu-rays, they were designed specifically for long-term archive storage. If you follow the link at the top of this thread you can get some more detailed information on them. They're supposed to last several hundred years, but of course no one has empirical evidence of that yet.
Our power was out for a week after a major storm in the area, but we got a generator about halfway through so it was really only three or four days.
Edit: When I was a kid my mom worked at a summer camp for two months out of the year and I came along too, there were only two buildings there with electricity.
Also check out Snow Crash which is considered one of the seminal works of cyberpunk. Same author, Neal Stephenson, and set in the same world though they're set about a century apart and are only very loosely linked.
Dune (1984)
The Fifth Element