There are some other options requiring more specialized, harder-to-find equipment that might be less susceptible to a Situation-X scenario.
Aside from Wifi there are a few other means of accessing the internet wirelessly:
and Satellite Internet
If you could access or assemble the equipment needed to make use of the networks these technologies compose, you could probably get online well after
Of course these technologies do have earth-based components, such as control centers, backbone links, satellite dishes, radio towers, cellular towers,
etc. So if these went you'd be SOL.
The safest of all, satellite internet, should theoretically survive any Situation-X not involving a planned and organized takeover by a government, or
nuclear war. It is also the hardest to access and the slowest.
Finally, you would have to consider this: just what would you find when you accessed the "internet"? Google's datacenters could probably survive
but the fact is that the huge majority of the internet is cable-based, and it is no longer redundant. If a major connection went
down, such as that to/from an ISP's datacenter, a backbone connection, it would cripple most everything in that subsection of the net. Or if the DNS
center went down, the internet would immediately cease to exist (as we know it).
Assuming a very-large-scale (multi-continent/hemisphere) disaster affecting the U.S. (where a good deal of the backbone connections and the DNS
servers are), In all likelihood there would be little accessible on the working internet, and you would be one of a only a handful of people on it if
connection required such equipment.
So unless there is something very very important that you foresee needing the internet for, it would probably be better to invest in radio as has been
However, in the true to-the-ends-of-the-earth spirit, if during/after a Situation-X of truly apocalyptic proportions, if some part of it was still
working, if you could get a connection, if, if, if... it would not be impossible. I'd suggest stocking up on technical books, everything you can find
on digital electronics, radio, radio-signaling, data transmission, internet communications, protocols, networks, etc. With the proper materials and
knowledge you could access the internet and use it for whatever ends you wanted, though at this level it would probably not be reading emails. This
would be hacking on a level unfathomable to most hackers, it would involve engineering and equipment that are at the peak of human achievement. It
makes for great sci-fi but it isn't practical.
An image comes to mind of Mad Max logging on to the internet with a massive salvaged desktop terminal and a 12" CRT.