The Internet may have augmented people's minds with the ability to find solutions to problems people already found solutions for. It's also, through things like BOINC and other distributed computing schemes, able to complete repetitive tasks on enormous amounts of data. The Internet, though, still can't actually solve a problem that nobody else has solved. It still requires people to do the actual thinking.
You're right, though, that the Internet can't be killed, at least not without wiping out a significant amount of our technology (massive EMP would do it). Even if a bunch of governments got together to strictly control, or completely wipe out the Internet people would band together and, within a few months or years, there would be a more robust, more independent Internet. Perhaps instead of using wires it'd use HAM radio (this idea already exists as the Hinternet). The Internet, as an idea, can't be killed. Things ON the Internet are also hard to kill (they killed suprnova only to be replaced a few days later with ten or fifteen copies, which were killed and replaced by more)
The Internet is like a virus or bacteria. What doesn't kill it makes it stronger, and since nothing can kill it (besides the aforementioned world-wide EMP) it's always getting stronger.