Internet can't go down that easily with simple attack or accident. The only reasons I can think of that can cause WHOLE network to fail are:

1. EMP attack of a large scale (and that won't affect whole internet, but can affect whole country)
2. Solar Flare Effect - the most dangerous catastrophe which can happen to us (this will however turn off ALL electricity on planet Earth down).

So with with internet down I would be worried more about my life than anything else as crisis preceding this event will most likely be huge.