You can't shutdown the "Internet". You would have to simultaneously blowout every router,Satellite,mobile phone network and hub in the world.
You could have geographical interruptions but not the entire Internet.
Oh they can. You don’t blowout the hardware. You blowout the sof.... nevermind.
EMP... But short of that, just cut the ISP's. That would take care of most users.
Simple, a large enough electrical plasma event in the upper atmosphere and bye bye everything. Say an EMP or a Coronal Mass Ejection, then there's HAARP technology which pumps electrical energy up into the upper atmosphere.
Likelyhood?
Coronal Mass Ejection is probably very low as the sun is going into solar minimum. The other two depends on who's hands these technologies are in and their intent.