The internet is NOT designed to survive a war, that's a urban myth. The first thing that would happen in such an event would be the deployment of the stash of Zero day exploits that every major power has saved up for the occasion.

December 7, 1941 was a peaceful Sunday, until it wasn't.

February 26, 1993 was just another Friday, until it wasn't.

September 11, 2001 was just another Tuesday, until it wasn't.

I was only a bit worried, but these type of events have a non-zero probability.