Cockroaches will in fact need bitcoin once the're the dominant species on this planet. If they intend on facilitating trade between regions of roach-earth, that is.

On the real though- Everything that has ever been built was once built from scratch, and can be rebuilt, physically and programmatically better. Precautions have been taken. Inevitably, there exists hard drives within Faraday cages belonging to proponents of mutual aid. The next level of postnuclear humans (or cockroaches if that's your flavor) will always stand on the (albeit perhaps crumbled) shoulders of giants.
EDIT:From what I understand, the main purpose of ARPANET- the internet's great uncle- was to allow communications in the event of a nuclear disaster.