I would be more concerned with businesses failing
Well, to be honest, most older businesses (and really important businesses) have a WAN, instead of going through the internet. The internet would be already set up jumps to the destination, and relied on constantly to be a backbone. In the event the ISP is down, there is no way to get data to the other side of the business. This is where the WAN comes through instead of the internet. The way they do that is wiring directly to the business, which is very costly, but brings in lower latencies and less jumps from network to network, and are virtually invincible to outside tampering. The only way this would go down is if one of the businesses had a hardware issue with their router. Business networks would still exist and eventually businesses would sell house-to-house communication lines, which means that in time, the internet would be back online.