I intended to tell you the net cannot easily be shut down, but I did some research:
The internet was originally created to survive Nuclear War, but "we" are not using that one now. Currently major sections could be shut down if underwater cables are cut.
There are projects to increase the number of satellites bringing the web to more parts of the world and some of them are proposed by private companies.

The modern web was built in a big hurry and is much more fragile than I expected. Hopefully major upgrades are coming soon.